LMFDB - Embedded newform 637.2.bl.b.534.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			534.8
Character	$\chi$	$=$	637.534
Dual form			637.2.bl.b.235.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79534 + 0.270604i) q^{2} +(-0.0106159 - 0.00723782i) q^{3} +(1.23888 - 0.382145i) q^{4} +(0.0531607 - 0.709380i) q^{5} +(0.0210178 + 0.0101216i) q^{6} +(-2.62131 + 0.358800i) q^{7} +(1.15083 - 0.554210i) q^{8} +(-1.09596 - 2.79247i) q^{9} +O(q^{10})$	\(q+(-1.79534 + 0.270604i) q^{2} +(-0.0106159 - 0.00723782i) q^{3} +(1.23888 - 0.382145i) q^{4} +(0.0531607 - 0.709380i) q^{5} +(0.0210178 + 0.0101216i) q^{6} +(-2.62131 + 0.358800i) q^{7} +(1.15083 - 0.554210i) q^{8} +(-1.09596 - 2.79247i) q^{9} +(0.0965197 + 1.28797i) q^{10} +(-1.14057 + 2.90613i) q^{11} +(-0.0159178 - 0.00490998i) q^{12} +(0.623490 + 0.781831i) q^{13} +(4.60905 - 1.35351i) q^{14} +(-0.00569871 + 0.00714596i) q^{15} +(-4.05857 + 2.76708i) q^{16} +(-0.265590 + 0.246431i) q^{17} +(2.72328 + 4.71686i) q^{18} +(1.13402 - 1.96417i) q^{19} +(-0.205226 - 0.899153i) q^{20} +(0.0304246 + 0.0151636i) q^{21} +(1.26131 - 5.52614i) q^{22} +(1.43798 + 1.33425i) q^{23} +(-0.0162284 - 0.00244604i) q^{24} +(4.44376 + 0.669789i) q^{25} +(-1.33094 - 1.23494i) q^{26} +(-0.0171539 + 0.0751561i) q^{27} +(-3.11038 + 1.44623i) q^{28} +(0.770039 + 3.37376i) q^{29} +(0.00829741 - 0.0143715i) q^{30} +(2.15961 + 3.74056i) q^{31} +(4.66504 - 4.32853i) q^{32} +(0.0331423 - 0.0225960i) q^{33} +(0.410139 - 0.514298i) q^{34} +(0.115175 + 1.87858i) q^{35} +(-2.42489 - 3.04072i) q^{36} +(-4.41717 - 1.36252i) q^{37} +(-1.50443 + 3.83323i) q^{38} +(-0.000960169 - 0.0128126i) q^{39} +(-0.331967 - 0.845837i) q^{40} +(-6.69285 + 3.22311i) q^{41} +(-0.0587258 - 0.0189908i) q^{42} +(6.11744 + 2.94600i) q^{43} +(-0.302473 + 4.03622i) q^{44} +(-2.03918 + 0.629004i) q^{45} +(-2.94272 - 2.00631i) q^{46} +(4.36897 - 0.658517i) q^{47} +0.0631131 q^{48} +(6.74252 - 1.88105i) q^{49} -8.15932 q^{50} +(0.00460310 - 0.000693806i) q^{51} +(1.07120 + 0.730334i) q^{52} +(-1.43383 + 0.442278i) q^{53} +(0.0104595 - 0.139573i) q^{54} +(2.00092 + 0.963591i) q^{55} +(-2.81783 + 1.86567i) q^{56} +(-0.0262550 + 0.0126437i) q^{57} +(-2.29544 - 5.84868i) q^{58} +(1.07582 + 14.3558i) q^{59} +(-0.00432924 + 0.0110307i) q^{60} +(9.39560 + 2.89816i) q^{61} +(-4.88946 - 6.13119i) q^{62} +(3.87480 + 6.92669i) q^{63} +(-1.07874 + 1.35270i) q^{64} +(0.587761 - 0.400728i) q^{65} +(-0.0533871 + 0.0495360i) q^{66} +(5.13903 + 8.90106i) q^{67} +(-0.234862 + 0.406793i) q^{68} +(-0.00560842 - 0.0245721i) q^{69} +(-0.715130 - 3.34152i) q^{70} +(-2.51776 + 11.0310i) q^{71} +(-2.80888 - 2.60626i) q^{72} +(3.16729 + 0.477393i) q^{73} +(8.29903 + 1.25088i) q^{74} +(-0.0423268 - 0.0392735i) q^{75} +(0.654314 - 2.86674i) q^{76} +(1.94707 - 8.02710i) q^{77} +(0.00519097 + 0.0227431i) q^{78} +(-2.61995 + 4.53789i) q^{79} +(1.74716 + 3.02617i) q^{80} +(-6.59638 + 6.12054i) q^{81} +(11.1438 - 7.59769i) q^{82} +(-10.3738 + 13.0084i) q^{83} +(0.0434871 + 0.00715928i) q^{84} +(0.160694 + 0.201504i) q^{85} +(-11.7801 - 3.63368i) q^{86} +(0.0162440 - 0.0413890i) q^{87} +(0.298003 + 3.97658i) q^{88} +(-0.759924 - 1.93625i) q^{89} +(3.49082 - 1.68109i) q^{90} +(-1.91488 - 1.82571i) q^{91} +(2.29136 + 1.10346i) q^{92} +(0.00414719 - 0.0553404i) q^{93} +(-7.66560 + 2.36453i) q^{94} +(-1.33306 - 0.908865i) q^{95} +(-0.0808528 + 0.0121866i) q^{96} +4.00692 q^{97} +(-11.5961 + 5.20169i) q^{98} +9.36530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.79534	+	0.270604i	−1.26950	+	0.191346i	−0.749031	−	0.662535i	$-0.769481\pi$
$2$	−1.79534	+	0.270604i	−1.26950	+	0.191346i	−0.520468	+	0.853881i	$0.674242\pi$
$3$	−0.0106159	−	0.00723782i	−0.00612911	−	0.00417875i	0.560252	−	0.828322i	$-0.310704\pi$
$3$	−0.0106159	−	0.00723782i	−0.00612911	−	0.00417875i	−0.566381	+	0.824144i	$0.691657\pi$
$4$	1.23888	−	0.382145i	0.619441	−	0.191072i
$5$	0.0531607	−	0.709380i	0.0237742	−	0.317244i	−0.972620	−	0.232401i	$-0.925342\pi$
$5$	0.0531607	−	0.709380i	0.0237742	−	0.317244i	0.996394	−	0.0848435i	$-0.0270390\pi$
$6$	0.0210178	+	0.0101216i	0.00858048	+	0.00413214i
$7$	−2.62131	+	0.358800i	−0.990762	+	0.135614i
$7$	−2.62131	+	0.358800i	−0.990762	+	0.135614i
$8$	1.15083	−	0.554210i	0.406880	−	0.195943i
$9$	−1.09596	−	2.79247i	−0.365321	−	0.930823i
$10$	0.0965197	+	1.28797i	0.0305222	+	0.407290i
$11$	−1.14057	+	2.90613i	−0.343895	+	0.876231i	0.649381	+	0.760463i	$0.275028\pi$
$11$	−1.14057	+	2.90613i	−0.343895	+	0.876231i	−0.993276	+	0.115768i	$0.963067\pi$
$12$	−0.0159178	−	0.00490998i	−0.00459506	−	0.00141739i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$14$	4.60905	−	1.35351i	1.23182	−	0.361740i
$15$	−0.00569871	+	0.00714596i	−0.00147140	+	0.00184508i
$16$	−4.05857	+	2.76708i	−1.01464	+	0.691771i
$17$	−0.265590	+	0.246431i	−0.0644150	+	0.0597683i	−0.711723	−	0.702460i	$-0.752085\pi$
$17$	−0.265590	+	0.246431i	−0.0644150	+	0.0597683i	0.647308	+	0.762228i	$0.275895\pi$
$18$	2.72328	+	4.71686i	0.641884	+	1.11178i
$19$	1.13402	−	1.96417i	0.260161	−	0.450612i	−0.706123	−	0.708089i	$-0.749558\pi$
$19$	1.13402	−	1.96417i	0.260161	−	0.450612i	0.966285	+	0.257476i	$0.0828910\pi$
$20$	−0.205226	−	0.899153i	−0.0458899	−	0.201057i
$21$	0.0304246	+	0.0151636i	0.00663918	+	0.00330896i
$22$	1.26131	−	5.52614i	0.268911	−	1.17818i
$23$	1.43798	+	1.33425i	0.299839	+	0.278210i	0.815716	−	0.578453i	$-0.196343\pi$
$23$	1.43798	+	1.33425i	0.299839	+	0.278210i	−0.515877	+	0.856663i	$0.672534\pi$
$24$	−0.0162284	−	0.00244604i	−0.00331261	−	0.000499295i
$25$	4.44376	+	0.669789i	0.888752	+	0.133958i
$26$	−1.33094	−	1.23494i	−0.261020	−	0.242191i
$27$	−0.0171539	+	0.0751561i	−0.00330127	+	0.0144638i
$28$	−3.11038	+	1.44623i	−0.587806	+	0.273312i
$29$	0.770039	+	3.37376i	0.142993	+	0.626492i	0.994731	+	0.102524i	$0.0326918\pi$
$29$	0.770039	+	3.37376i	0.142993	+	0.626492i	−0.851738	+	0.523968i	$0.824451\pi$
$30$	0.00829741	−	0.0143715i	0.00151489	−	0.00262387i
$31$	2.15961	+	3.74056i	0.387878	+	0.671824i	0.992164	−	0.124943i	$-0.0398748\pi$
$31$	2.15961	+	3.74056i	0.387878	+	0.671824i	−0.604286	+	0.796768i	$0.706542\pi$
$32$	4.66504	−	4.32853i	0.824671	−	0.765183i
$33$	0.0331423	−	0.0225960i	0.00576933	−	0.00393346i
$34$	0.410139	−	0.514298i	0.0703383	−	0.0882014i
$35$	0.115175	+	1.87858i	0.0194681	+	0.317538i
$36$	−2.42489	−	3.04072i	−0.404149	−	0.506787i
$37$	−4.41717	−	1.36252i	−0.726178	−	0.223996i	−0.0904408	−	0.995902i	$-0.528828\pi$
$37$	−4.41717	−	1.36252i	−0.726178	−	0.223996i	−0.635737	+	0.771906i	$0.719304\pi$
$38$	−1.50443	+	3.83323i	−0.244051	+	0.621833i
$39$	−0.000960169	−	0.0128126i	−0.000153750	−	0.00205165i
$40$	−0.331967	−	0.845837i	−0.0524885	−	0.133739i
$41$	−6.69285	+	3.22311i	−1.04525	+	0.503365i	−0.876051	−	0.482218i	$-0.839831\pi$
$41$	−6.69285	+	3.22311i	−1.04525	+	0.503365i	−0.169196	+	0.985582i	$0.554117\pi$
$42$	−0.0587258	−	0.0189908i	−0.00906159	−	0.00293034i
$43$	6.11744	+	2.94600i	0.932901	+	0.449262i	0.837660	−	0.546193i	$-0.183923\pi$
$43$	6.11744	+	2.94600i	0.932901	+	0.449262i	0.0952416	+	0.995454i	$0.469638\pi$
$44$	−0.302473	+	4.03622i	−0.0455995	+	0.608482i
$45$	−2.03918	+	0.629004i	−0.303983	+	0.0937664i
$46$	−2.94272	−	2.00631i	−0.433880	−	0.295814i
$47$	4.36897	−	0.658517i	0.637280	−	0.0960545i	0.177548	−	0.984112i	$-0.443184\pi$
$47$	4.36897	−	0.658517i	0.637280	−	0.0960545i	0.459732	+	0.888058i	$0.347945\pi$
$48$	0.0631131			0.00910959
$49$	6.74252	−	1.88105i	0.963218	−	0.268722i
$50$	−8.15932			−1.15390
$51$	0.00460310		0.000693806i	0.000644563		9.71523e-5i
$52$	1.07120	+	0.730334i	0.148549	+	0.101279i
$53$	−1.43383	+	0.442278i	−0.196952	+	0.0607516i	−0.391662	−	0.920109i	$-0.628100\pi$
$53$	−1.43383	+	0.442278i	−0.196952	+	0.0607516i	0.194710	+	0.980861i	$0.437623\pi$
$54$	0.0104595	−	0.139573i	0.00142336	−	0.0189935i
$55$	2.00092	+	0.963591i	0.269804	+	0.129931i
$56$	−2.81783	+	1.86567i	−0.376548	+	0.249311i
$57$	−0.0262550	+	0.0126437i	−0.00347755	+	0.00167470i
$58$	−2.29544	−	5.84868i	−0.301406	−	0.767970i
$59$	1.07582	+	14.3558i	0.140060	+	1.86897i	0.418101	+	0.908401i	$0.362696\pi$
$59$	1.07582	+	14.3558i	0.140060	+	1.86897i	−0.278041	+	0.960569i	$0.589685\pi$
$60$	−0.00432924	+	0.0110307i	−0.000558903	+	0.00142406i
$61$	9.39560	+	2.89816i	1.20298	+	0.371071i	0.830527	−	0.556979i	$-0.188040\pi$
$61$	9.39560	+	2.89816i	1.20298	+	0.371071i	0.372456	+	0.928050i	$0.378516\pi$
$62$	−4.88946	−	6.13119i	−0.620962	−	0.778661i
$63$	3.87480	+	6.92669i	0.488178	+	0.872681i
$64$	−1.07874	+	1.35270i	−0.134843	+	0.169088i
$65$	0.587761	−	0.400728i	0.0729027	−	0.0497042i
$66$	−0.0533871	+	0.0495360i	−0.00657150	+	0.00609746i
$67$	5.13903	+	8.90106i	0.627832	+	1.08744i	0.987986	+	0.154544i	$0.0493909\pi$
$67$	5.13903	+	8.90106i	0.627832	+	1.08744i	−0.360154	+	0.932893i	$0.617276\pi$
$68$	−0.234862	+	0.406793i	−0.0284812	+	0.0493309i
$69$	−0.00560842	−	0.0245721i	−0.000675175	−	0.00295813i
$70$	−0.715130	−	3.34152i	−0.0854744	−	0.399389i
$71$	−2.51776	+	11.0310i	−0.298803	+	1.30914i	0.573108	+	0.819480i	$0.305737\pi$
$71$	−2.51776	+	11.0310i	−0.298803	+	1.30914i	−0.871912	+	0.489663i	$0.837120\pi$
$72$	−2.80888	−	2.60626i	−0.331030	−	0.307151i
$73$	3.16729	+	0.477393i	0.370704	+	0.0558746i	0.331752	−	0.943367i	$-0.392360\pi$
$73$	3.16729	+	0.477393i	0.370704	+	0.0558746i	0.0389514	+	0.999241i	$0.487598\pi$
$74$	8.29903	+	1.25088i	0.964743	+	0.145412i
$75$	−0.0423268	−	0.0392735i	−0.00488748	−	0.00453492i
$76$	0.654314	−	2.86674i	0.0750550	−	0.328837i
$77$	1.94707	−	8.02710i	0.221889	−	0.914773i
$78$	0.00519097	+	0.0227431i	0.000587762	+	0.00257515i
$79$	−2.61995	+	4.53789i	−0.294767	+	0.510552i	−0.974931	−	0.222509i	$-0.928575\pi$
$79$	−2.61995	+	4.53789i	−0.294767	+	0.510552i	0.680163	+	0.733061i	$0.261909\pi$
$80$	1.74716	+	3.02617i	0.195338	+	0.338336i
$81$	−6.59638	+	6.12054i	−0.732931	+	0.680060i
$82$	11.1438	−	7.59769i	1.23062	−	0.839025i
$83$	−10.3738	+	13.0084i	−1.13868	+	1.42786i	−0.250644	+	0.968079i	$0.580642\pi$
$83$	−10.3738	+	13.0084i	−1.13868	+	1.42786i	−0.888034	+	0.459777i	$0.847929\pi$
$84$	0.0434871	+	0.00715928i	0.00474483	+	0.000781142i
$85$	0.160694	+	0.201504i	0.0174298	+	0.0218562i
$86$	−11.7801	−	3.63368i	−1.27028	−	0.391830i
$87$	0.0162440	−	0.0413890i	0.00174154	−	0.00443737i
$88$	0.298003	+	3.97658i	0.0317672	+	0.423904i
$89$	−0.759924	−	1.93625i	−0.0805517	−	0.205242i	0.884924	−	0.465735i	$-0.154210\pi$
$89$	−0.759924	−	1.93625i	−0.0805517	−	0.205242i	−0.965476	+	0.260493i	$0.916115\pi$
$90$	3.49082	−	1.68109i	0.367965	−	0.177202i
$91$	−1.91488	−	1.82571i	−0.200734	−	0.191387i
$92$	2.29136	+	1.10346i	0.238891	+	0.115044i
$93$	0.00414719	−	0.0553404i	0.000430043	−	0.00573853i
$94$	−7.66560	+	2.36453i	−0.790647	+	0.243882i
$95$	−1.33306	−	0.908865i	−0.136769	−	0.0932476i
$96$	−0.0808528	+	0.0121866i	−0.00825201	+	0.00124379i
$97$	4.00692			0.406841			0.203421	−	0.979091i	$-0.434794\pi$
$97$	4.00692			0.406841			0.203421	+	0.979091i	$0.434794\pi$
$98$	−11.5961	+	5.20169i	−1.17139	+	0.525450i
$99$	9.36530			0.941248
$100$	5.76125	−	0.868369i	0.576125	−	0.0868369i
$101$	0.603608	+	0.411533i	0.0600613	+	0.0409491i	0.592978	−	0.805218i	$-0.297952\pi$
$101$	0.603608	+	0.411533i	0.0600613	+	0.0409491i	−0.532917	+	0.846167i	$0.678904\pi$
$102$	−0.00807640	+	0.00249124i	−0.000799683	+	0.000246669i
$103$	0.989212	−	13.2001i	0.0974699	−	1.30065i	−0.707238	−	0.706975i	$-0.750059\pi$
$103$	0.989212	−	13.2001i	0.0974699	−	1.30065i	0.804708	−	0.593671i	$-0.202322\pi$
$104$	1.15083	+	0.554210i	0.112848	+	0.0543448i
$105$	0.0123741	−	0.0207765i	0.00120759	−	0.00202757i
$106$	2.45454	−	1.18204i	0.238406	−	0.114810i
$107$	−2.34028	−	5.96293i	−0.226243	−	0.576459i	0.772005	−	0.635616i	$-0.219254\pi$
$107$	−2.34028	−	5.96293i	−0.226243	−	0.576459i	−0.998249	+	0.0591575i	$0.981159\pi$
$108$	0.00746884	+	0.0996648i	0.000718690	+	0.00959025i
$109$	−1.07531	+	2.73984i	−0.102996	+	0.262429i	−0.973077	−	0.230479i	$-0.925971\pi$
$109$	−1.07531	+	2.73984i	−0.102996	+	0.262429i	0.870082	+	0.492908i	$0.164066\pi$
$110$	−3.85308	−	1.18852i	−0.367377	−	0.113321i
$111$	0.0370307	+	0.0464350i	0.00351480	+	0.00440742i
$112$	9.64593	−	8.70960i	0.911455	−	0.822980i
$113$	3.61702	−	4.53560i	0.340260	−	0.426673i	−0.582032	−	0.813166i	$-0.697742\pi$
$113$	3.61702	−	4.53560i	0.340260	−	0.426673i	0.922292	+	0.386493i	$0.126314\pi$
$114$	0.0437152	−	0.0298045i	0.00409430	−	0.00279145i
$115$	1.02293	−	0.949143i	0.0953890	−	0.0885080i
$116$	2.24325	+	3.88543i	0.208281	+	0.360753i
$117$	1.49992	−	2.59793i	0.138667	−	0.240179i
$118$	−5.81622	−	25.4825i	−0.535426	−	2.34585i
$119$	0.607773	−	0.741266i	0.0557145	−	0.0679517i
$120$	−0.00259788	+	0.0113821i	−0.000237153	+	0.00103903i
$121$	0.918882	+	0.852598i	0.0835347	+	0.0775089i
$122$	−17.6526	−	2.66070i	−1.59819	−	0.240888i
$123$	0.0943790	+	0.0142254i	0.00850987	+	0.00128266i
$124$	4.10494	+	3.80883i	0.368635	+	0.342043i
$125$	1.50284	−	6.58438i	0.134418	−	0.588924i
$126$	−8.83098	−	11.3872i	−0.786726	−	1.01446i
$127$	−1.53469	−	6.72391i	−0.136182	−	0.596650i	−0.996254	−	0.0864780i	$-0.972439\pi$
$127$	−1.53469	−	6.72391i	−0.136182	−	0.596650i	0.860072	−	0.510172i	$-0.170418\pi$
$128$	−4.79320	+	8.30206i	−0.423663	+	0.733805i
$129$	−0.0436197	−	0.0755515i	−0.00384050	−	0.00665194i
$130$	−0.946793	+	0.878495i	−0.0830392	+	0.0770491i
$131$	6.16845	−	4.20558i	0.538940	−	0.367443i	−0.263049	−	0.964783i	$-0.584728\pi$
$131$	6.16845	−	4.20558i	0.538940	−	0.367443i	0.801988	+	0.597340i	$0.203776\pi$
$132$	0.0324244	−	0.0406589i	0.00282218	−	0.00353891i
$133$	−2.26786	+	5.55559i	−0.196648	+	0.481731i
$134$	−11.6350	−	14.5898i	−1.00511	−	1.26037i
$135$	0.0524023	+	0.0161640i	0.00451007	+	0.00139117i
$136$	−0.169074	+	0.430793i	−0.0144979	+	0.0369402i
$137$	0.166648	+	2.22376i	0.0142377	+	0.189989i	0.999788	+	0.0206042i	$0.00655899\pi$
$137$	0.166648	+	2.22376i	0.0142377	+	0.189989i	−0.985550	+	0.169385i	$0.945822\pi$
$138$	0.0167184	+	0.0425977i	0.00142316	+	0.00362615i
$139$	−3.56667	+	1.71762i	−0.302521	+	0.145686i	−0.578986	−	0.815338i	$-0.696551\pi$
$139$	−3.56667	+	1.71762i	−0.302521	+	0.145686i	0.276465	+	0.961024i	$0.410837\pi$
$140$	0.860577	+	2.28332i	0.0727320	+	0.192976i
$141$	−0.0511469	−	0.0246310i	−0.00430735	−	0.00207431i
$142$	1.53520	−	20.4858i	0.128831	−	1.71913i
$143$	−2.98324	+	0.920207i	−0.249471	+	0.0769516i
$144$	12.1750	+	8.30079i	1.01459	+	0.691733i
$145$	2.43421	−	0.366899i	0.202151	−	0.0304693i
$146$	−5.81556			−0.481299
$147$	−0.0851929	−	0.0288320i	−0.00702659	−	0.00237803i
$148$	−5.99303			−0.492624
$149$	−19.0031	+	2.86425i	−1.55679	+	0.234649i	−0.870313	−	0.492499i	$-0.836083\pi$
$149$	−19.0031	+	2.86425i	−1.55679	+	0.234649i	−0.686481	+	0.727148i	$0.740845\pi$
$150$	0.0866187	+	0.0590556i	0.00707239	+	0.00482187i
$151$	18.8660	−	5.81938i	1.53529	−	0.473574i	0.592110	−	0.805857i	$-0.298295\pi$
$151$	18.8660	−	5.81938i	1.53529	−	0.473574i	0.943180	+	0.332283i	$0.107819\pi$
$152$	0.216494	−	2.88891i	0.0175600	−	0.234322i
$153$	0.979227	+	0.471571i	0.0791658	+	0.0381243i
$154$	−1.32349	+	14.9383i	−0.106650	+	1.20376i
$155$	2.76828	−	1.33314i	0.222354	−	0.107080i
$156$	−0.00608579	−	0.0155063i	−0.000487253	−	0.00124150i
$157$	−1.06759	−	14.2460i	−0.0852029	−	1.13695i	−0.861900	−	0.507079i	$-0.830725\pi$
$157$	−1.06759	−	14.2460i	−0.0852029	−	1.13695i	0.776697	−	0.629875i	$-0.216894\pi$
$158$	3.47573	−	8.85603i	0.276515	−	0.704548i
$159$	0.0184226	+	0.00568261i	0.00146101	+	0.000450660i
$160$	−2.82257	−	3.53939i	−0.223144	−	0.279814i
$161$	−4.24811	−	2.98153i	−0.334798	−	0.234978i
$162$	10.1865	−	12.7735i	0.800328	−	1.00358i
$163$	13.6404	−	9.29987i	1.06840	−	0.728422i	0.104456	−	0.994530i	$-0.466690\pi$
$163$	13.6404	−	9.29987i	1.06840	−	0.728422i	0.963943	+	0.266107i	$0.0857376\pi$
$164$	−7.05996	+	6.55068i	−0.551290	+	0.511523i
$165$	−0.0142673	−	0.0247117i	−0.00111071	−	0.00192380i
$166$	15.1045	−	26.1617i	1.17234	−	2.03054i
$167$	−3.20961	−	14.0622i	−0.248367	−	1.08817i	−0.933169	−	0.359439i	$-0.882968\pi$
$167$	−3.20961	−	14.0622i	−0.248367	−	1.08817i	0.684801	−	0.728730i	$-0.259889\pi$
$168$	0.0434173		0.000589069i	0.00334971		4.54476e-5i
$169$	−0.222521	+	0.974928i	−0.0171170	+	0.0749945i
$170$	−0.343029	−	0.318285i	−0.0263092	−	0.0244113i
$171$	−6.72773	−	1.01404i	−0.514482	−	0.0775457i
$172$	8.70459	+	1.31201i	0.663719	+	0.100039i
$173$	−1.99910	−	1.85489i	−0.151988	−	0.141025i	0.600514	−	0.799614i	$-0.294963\pi$
$173$	−1.99910	−	1.85489i	−0.151988	−	0.141025i	−0.752502	+	0.658590i	$0.771153\pi$
$174$	−0.0179635	+	0.0787031i	−0.00136181	+	0.00596647i
$175$	−11.8888	−	0.161303i	−0.898708	−	0.0121933i
$176$	−3.41242	−	14.9508i	−0.257221	−	1.12696i
$177$	0.0924840	−	0.160187i	0.00695152	−	0.0120404i
$178$	1.88828	+	3.27060i	0.141533	+	0.245142i
$179$	0.721017	−	0.669006i	0.0538914	−	0.0500039i	−0.652767	−	0.757558i	$-0.726392\pi$
$179$	0.721017	−	0.669006i	0.0538914	−	0.0500039i	0.706659	+	0.707555i	$0.250202\pi$
$180$	−2.28594	+	1.55852i	−0.170384	+	0.116166i
$181$	8.54470	−	10.7147i	0.635122	−	0.796418i	−0.355261	−	0.934767i	$-0.615608\pi$
$181$	8.54470	−	10.7147i	0.635122	−	0.796418i	0.990384	+	0.138349i	$0.0441795\pi$
$182$	3.93191	+	2.75961i	0.291453	+	0.204556i
$183$	−0.0787666	−	0.0987702i	−0.00582260	−	0.00730131i
$184$	2.39432	+	0.738550i	0.176512	+	0.0544466i
$185$	−1.20136	+	3.06102i	−0.0883258	+	0.225050i
$186$	0.00752973	+	0.100477i	0.000552106	+	0.00736735i
$187$	−0.413237	−	1.05291i	−0.0302189	−	0.0769965i
$188$	5.16099	−	2.48540i	0.376404	−	0.181267i
$189$	0.0179996	−	0.203162i	0.00130928	−	0.0147779i
$190$	2.63924	+	1.27099i	0.191471	+	0.0922074i
$191$	−0.858718	+	11.4588i	−0.0621347	+	0.829129i	0.875879	+	0.482531i	$0.160282\pi$
$191$	−0.858718	+	11.4588i	−0.0621347	+	0.829129i	−0.938014	+	0.346599i	$0.887337\pi$
$192$	0.0212425	−	0.00655243i	0.00153304	−	0.000472881i
$193$	−11.8074	−	8.05015i	−0.849915	−	0.579462i	0.0581421	−	0.998308i	$-0.481482\pi$
$193$	−11.8074	−	8.05015i	−0.849915	−	0.579462i	−0.908057	+	0.418846i	$0.862435\pi$
$194$	−7.19380	+	1.08429i	−0.516485	+	0.0778475i
$195$	−0.00914002			−0.000654531
$196$	7.63436	−	4.90702i	0.545311	−	0.350501i
$197$	−11.7957			−0.840411			−0.420205	−	0.907429i	$-0.638042\pi$
$197$	−11.7957			−0.840411			−0.420205	+	0.907429i	$0.638042\pi$
$198$	−16.8139	+	2.53429i	−1.19491	+	0.180104i
$199$	12.0277	+	8.20033i	0.852619	+	0.581306i	0.908855	−	0.417111i	$-0.136958\pi$
$199$	12.0277	+	8.20033i	0.852619	+	0.581306i	−0.0562360	+	0.998418i	$0.517910\pi$
$200$	5.48521	−	1.69196i	0.387863	−	0.119640i
$201$	0.00986867	−	0.131688i	0.000696082	−	0.00928857i
$202$	−1.19505	−	0.575504i	−0.0840832	−	0.0404923i
$203$	−3.22902	−	8.56738i	−0.226633	−	0.601312i
$204$	0.00543757	−	0.00261859i	0.000380706	−	0.000183338i
$205$	1.93061	+	4.91911i	0.134840	+	0.343566i
$206$	1.79603	+	23.9664i	0.125136	+	1.66982i
$207$	2.14988	−	5.47779i	0.149427	−	0.380733i
$208$	−4.69387	−	1.44787i	−0.325461	−	0.100391i
$209$	4.41472	+	5.53588i	0.305372	+	0.382925i
$210$	−0.0165936	+	0.0406493i	−0.00114506	+	0.00280507i
$211$	−12.6713	+	15.8893i	−0.872329	+	1.09387i	0.122516	+	0.992466i	$0.460904\pi$
$211$	−12.6713	+	15.8893i	−0.872329	+	1.09387i	−0.994846	+	0.101400i	$0.967668\pi$
$212$	−1.60733	+	1.09586i	−0.110392	+	0.0752641i
$213$	0.106569	−	0.0988815i	0.00730198	−	0.00677525i
$214$	5.81520	+	10.0722i	0.397519	+	0.688523i
$215$	2.41504	−	4.18298i	0.164705	−	0.285277i
$216$	0.0219111	+	0.0959987i	0.00149086	+	0.00653188i
$217$	−7.00313	−	9.03030i	−0.475403	−	0.613016i
$218$	1.18913	−	5.20994i	0.0805383	−	0.352861i
$219$	−0.0301685	−	0.0279923i	−0.00203860	−	0.00189154i
$220$	2.84713	+	0.429136i	0.191954	+	0.0289323i
$221$	−0.358260	−	0.0539990i	−0.0240992	−	0.00363237i
$222$	−0.0790483	−	0.0733461i	−0.00530537	−	0.00492267i
$223$	−1.06303	+	4.65743i	−0.0711856	+	0.311885i	−0.997968	−	0.0637136i	$-0.979706\pi$
$223$	−1.06303	+	4.65743i	−0.0711856	+	0.311885i	0.926783	+	0.375598i	$0.122563\pi$
$224$	−10.6754	+	13.0202i	−0.713283	+	0.869950i
$225$	−2.99983	−	13.1431i	−0.199989	−	0.876208i
$226$	−5.26643	+	9.12173i	−0.350318	+	0.606768i
$227$	8.49907	+	14.7208i	0.564103	+	0.977055i	0.997133	+	0.0756751i	$0.0241112\pi$
$227$	8.49907	+	14.7208i	0.564103	+	0.977055i	−0.433030	+	0.901380i	$0.642555\pi$
$228$	−0.0276951	+	0.0256973i	−0.00183415	+	0.00170184i
$229$	−21.6201	+	14.7403i	−1.42870	+	0.974069i	−0.431282	+	0.902217i	$0.641939\pi$
$229$	−21.6201	+	14.7403i	−1.42870	+	0.974069i	−0.997415	+	0.0718521i	$0.977109\pi$
$230$	−1.57967	+	1.98085i	−0.104161	+	0.130613i
$231$	−0.0787687	+	0.0711226i	−0.00518260	+	0.00467952i
$232$	2.75596	+	3.45586i	0.180937	+	0.226888i
$233$	1.18972	+	0.366981i	0.0779415	+	0.0240418i	0.333481	−	0.942757i	$-0.391777\pi$
$233$	1.18972	+	0.366981i	0.0779415	+	0.0240418i	−0.255539	+	0.966799i	$0.582253\pi$
$234$	−1.98985	+	5.07006i	−0.130081	+	0.331440i
$235$	−0.234881	−	3.13427i	−0.0153219	−	0.204457i
$236$	6.81882	+	17.3741i	0.443867	+	1.13095i
$237$	0.0606576	−	0.0292111i	0.00394013	−	0.00189747i
$238$	−0.890571	+	1.49529i	−0.0577271	+	0.0969254i
$239$	−16.7382	−	8.06069i	−1.08270	−	0.521403i	−0.194523	−	0.980898i	$-0.562316\pi$
$239$	−16.7382	−	8.06069i	−1.08270	−	0.521403i	−0.888180	+	0.459495i	$0.848030\pi$
$240$	0.00335513	−	0.0447711i	0.000216573	−	0.00288997i
$241$	−2.40855	+	0.742940i	−0.155148	+	0.0478569i	−0.371357	−	0.928490i	$-0.621107\pi$
$241$	−2.40855	+	0.742940i	−0.155148	+	0.0478569i	0.216208	+	0.976347i	$0.430631\pi$
$242$	−1.88042	−	1.28205i	−0.120878	−	0.0824134i
$243$	0.343010	−	0.0517004i	0.0220041	−	0.00331658i
$244$	12.7476			0.816078
$245$	−0.975943	−	4.88301i	−0.0623507	−	0.311964i
$246$	−0.173292			−0.0110487
$247$	2.24270	−	0.338033i	0.142700	−	0.0215085i
$248$	4.55840	+	3.10787i	0.289459	+	0.197350i
$249$	0.204280	−	0.0630121i	0.0129457	−	0.00399323i
$250$	−0.916353	+	12.2279i	−0.0579553	+	0.773359i
$251$	5.38798	+	2.59471i	0.340086	+	0.163777i	0.596129	−	0.802889i	$-0.296705\pi$
$251$	5.38798	+	2.59471i	0.340086	+	0.163777i	−0.256043	+	0.966665i	$0.582419\pi$
$252$	7.44741	+	7.10062i	0.469143	+	0.447297i
$253$	−5.51762	+	2.65714i	−0.346890	+	0.167053i
$254$	4.57481	+	11.6564i	0.287049	+	0.731389i
$255$	−0.000247468	−	0.00330223i	−1.54971e−5	−	0.000206794i
$256$	7.62306	−	19.4232i	0.476441	−	1.21395i
$257$	6.34765	+	1.95799i	0.395955	+	0.122136i	0.486337	−	0.873771i	$-0.338333\pi$
$257$	6.34765	+	1.95799i	0.395955	+	0.122136i	−0.0903819	+	0.995907i	$0.528809\pi$
$258$	0.0987568	+	0.123837i	0.00614833	+	0.00770976i
$259$	12.0676	+	1.98669i	0.749846	+	0.123447i
$260$	0.575030	−	0.721065i	0.0356618	−	0.0447185i
$261$	8.57719	−	5.84783i	0.530915	−	0.361971i
$262$	−9.93643	+	9.21966i	−0.613875	+	0.569592i
$263$	11.0414	+	19.1243i	0.680845	+	1.17926i	0.974723	+	0.223415i	$0.0717205\pi$
$263$	11.0414	+	19.1243i	0.680845	+	1.17926i	−0.293879	+	0.955843i	$0.594946\pi$
$264$	0.0256181	−	0.0443719i	0.00157669	−	0.00273090i
$265$	0.237520	+	1.04064i	0.0145907	+	0.0639262i
$266$	2.56822	−	10.5879i	0.157468	−	0.649185i
$267$	−0.00594695	+	0.0260553i	−0.000363948	+	0.00159456i
$268$	9.76814	+	9.06351i	0.596684	+	0.553642i
$269$	−5.27420	−	0.794958i	−0.321574	−	0.0484695i	−0.0137282	−	0.999906i	$-0.504370\pi$
$269$	−5.27420	−	0.794958i	−0.321574	−	0.0484695i	−0.307846	+	0.951436i	$0.599608\pi$
$270$	−0.0984541	−	0.0148396i	−0.00599173	−	0.000903107i
$271$	12.2737	+	11.3883i	0.745574	+	0.691792i	0.958441	−	0.285289i	$-0.0920897\pi$
$271$	12.2737	+	11.3883i	0.745574	+	0.691792i	−0.212867	+	0.977081i	$0.568280\pi$
$272$	0.396018	−	1.73507i	0.0240121	−	0.105204i
$273$	0.00711405	+	0.0332412i	0.000430562	+	0.00201185i
$274$	−0.900950	−	3.94732i	−0.0544284	−	0.238466i
$275$	−7.01492	+	12.1502i	−0.423016	+	0.732685i
$276$	−0.0163383	−	0.0282987i	−0.000983448	−	0.00170338i
$277$	−18.7453	+	17.3931i	−1.12630	+	1.04505i	−0.127717	+	0.991811i	$0.540765\pi$
$277$	−18.7453	+	17.3931i	−1.12630	+	1.04505i	−0.998582	+	0.0532418i	$0.983045\pi$
$278$	5.93859	−	4.04886i	0.356173	−	0.242835i
$279$	8.07854	−	10.1302i	0.483649	−	0.606477i
$280$	1.17367	+	2.09809i	0.0701404	+	0.125385i
$281$	8.54294	+	10.7125i	0.509629	+	0.639055i	0.968371	−	0.249515i	$-0.0802712\pi$
$281$	8.54294	+	10.7125i	0.509629	+	0.639055i	−0.458742	+	0.888570i	$0.651700\pi$
$282$	0.0984915	+	0.0303806i	0.00586508	+	0.00180914i
$283$	9.20659	−	23.4580i	0.547275	−	1.39443i	−0.343140	−	0.939284i	$-0.611491\pi$
$283$	9.20659	−	23.4580i	0.547275	−	1.39443i	0.890415	−	0.455150i	$-0.150414\pi$
$284$	1.09624	+	14.6283i	0.0650498	+	0.868030i
$285$	0.00757347	+	0.0192969i	0.000448614	+	0.00114305i
$286$	5.10692	−	2.45936i	0.301979	−	0.145425i
$287$	16.3876	−	10.8502i	0.967328	−	0.640464i
$288$	−17.2000	−	8.28308i	−1.01352	−	0.488085i
$289$	−1.26060	+	16.8216i	−0.0741531	+	0.989504i
$290$	−4.27096	+	1.31742i	−0.250800	+	0.0773614i
$291$	−0.0425372	−	0.0290014i	−0.00249357	−	0.00170009i
$292$	4.10634	−	0.618931i	0.240305	−	0.0362202i
$293$	27.8290			1.62579			0.812894	−	0.582412i	$-0.197891\pi$
$293$	27.8290			1.62579			0.812894	+	0.582412i	$0.197891\pi$
$294$	0.160752	+	0.0287098i	0.00937527	+	0.00167439i
$295$	10.2409			0.596250
$296$	−5.83853	+	0.880016i	−0.339357	+	0.0511499i
$297$	−0.198848	−	0.135572i	−0.0115383	−	0.00786671i
$298$	33.3420	−	10.2846i	1.93145	−	0.595773i
$299$	−0.146593	+	1.95615i	−0.00847769	+	0.113127i
$300$	−0.0674461	−	0.0324803i	−0.00389400	−	0.00187525i
$301$	−17.0927	−	5.52745i	−0.985209	−	0.318597i
$302$	−32.2961	+	15.5530i	−1.85843	+	0.894974i
$303$	−0.00342926	−	0.00873761i	−0.000197006	−	0.000501963i
$304$	0.832553	+	11.1096i	0.0477502	+	0.637182i
$305$	2.55537	−	6.51098i	0.146320	−	0.372818i
$306$	−1.88566	−	0.581648i	−0.107796	−	0.0332506i
$307$	−12.4817	−	15.6516i	−0.712371	−	0.893285i	0.285508	−	0.958376i	$-0.407838\pi$
$307$	−12.4817	−	15.6516i	−0.712371	−	0.893285i	−0.997879	+	0.0650913i	$0.979266\pi$
$308$	−0.655321	−	10.6887i	−0.0373404	−	0.609045i
$309$	−0.106041	+	0.132972i	−0.00603248	+	0.00756450i
$310$	−4.60927	+	3.14254i	−0.261789	+	0.178485i
$311$	11.9980	−	11.1325i	0.680345	−	0.631267i	−0.262331	−	0.964978i	$-0.584491\pi$
$311$	11.9980	−	11.1325i	0.680345	−	0.631267i	0.942676	+	0.333710i	$0.108301\pi$
$312$	−0.00820585	−	0.0142129i	−0.000464565	−	0.000804649i
$313$	5.80745	−	10.0588i	0.328256	−	0.568557i	−0.653910	−	0.756573i	$-0.726872\pi$
$313$	5.80745	−	10.0588i	0.328256	−	0.568557i	0.982166	+	0.188016i	$0.0602057\pi$
$314$	5.77171	+	25.2875i	0.325717	+	1.42706i
$315$	5.11964	−	2.38047i	0.288459	−	0.134125i
$316$	−1.51168	+	6.62310i	−0.0850387	+	0.372579i
$317$	−2.97588	−	2.76121i	−0.167142	−	0.155085i	0.592167	−	0.805815i	$-0.298273\pi$
$317$	−2.97588	−	2.76121i	−0.167142	−	0.155085i	−0.759309	+	0.650730i	$0.774463\pi$
$318$	−0.0346126	−	0.00521701i	−0.00194098	−	0.000292555i
$319$	−10.6829	−	1.61018i	−0.598126	−	0.0901530i
$320$	0.902232	+	0.837149i	0.0504363	+	0.0467981i
$321$	−0.0183144	+	0.0802406i	−0.00102221	+	0.00447859i
$322$	8.43363	+	4.20331i	0.469988	+	0.234241i
$323$	0.182851	+	0.801121i	0.0101741	+	0.0445756i
$324$	−5.83320	+	10.1034i	−0.324067	+	0.561300i
$325$	2.24698	+	3.89188i	0.124640	+	0.215883i
$326$	−21.9726	+	20.3876i	−1.21695	+	1.12917i
$327$	0.0312459	−	0.0213031i	0.00172790	−	0.00117806i
$328$	−5.91605	+	7.41849i	−0.326659	+	0.409618i
$329$	−11.2162	+	3.29376i	−0.618366	+	0.181591i
$330$	0.0323018	+	0.0405051i	0.00177815	+	0.00222973i
$331$	1.33592	+	0.412077i	0.0734289	+	0.0226498i	0.331252	−	0.943542i	$-0.392529\pi$
$331$	1.33592	+	0.412077i	0.0734289	+	0.0226498i	−0.257823	+	0.966192i	$0.583005\pi$
$332$	−7.88089	+	20.0802i	−0.432520	+	1.10204i
$333$	1.03627	+	13.8281i	0.0567873	+	0.757773i
$334$	9.56766	+	24.3780i	0.523519	+	1.33390i
$335$	6.58742	−	3.17234i	0.359909	−	0.173323i
$336$	−0.165439	+	0.0226450i	−0.00902543	+	0.00123539i
$337$	−7.05602	−	3.39800i	−0.384366	−	0.185101i	0.231715	−	0.972784i	$-0.425566\pi$
$337$	−7.05602	−	3.39800i	−0.384366	−	0.185101i	−0.616081	+	0.787683i	$0.711281\pi$
$338$	0.135682	−	1.81054i	0.00738010	−	0.0984806i
$339$	−0.0712258	+	0.0219703i	−0.00386845	+	0.00119326i
$340$	0.276085	+	0.188232i	0.0149728	+	0.0102083i
$341$	−13.3338	+	2.00974i	−0.722063	+	0.108833i
$342$	12.3530			0.667973
$343$	−16.9993	+	7.35004i	−0.917877	+	0.396865i
$344$	8.67284			0.467608
$345$	−0.0177291	+	0.00267223i	−0.000954503	+	0.000143868i
$346$	4.09100	+	2.78920i	0.219934	+	0.149948i
$347$	−5.34836	+	1.64975i	−0.287115	+	0.0885632i	−0.434967	−	0.900446i	$-0.643240\pi$
$347$	−5.34836	+	1.64975i	−0.287115	+	0.0885632i	0.147852	+	0.989009i	$0.452764\pi$
$348$	0.00430780	−	0.0574836i	0.000230923	−	0.00308145i
$349$	11.0909	+	5.34109i	0.593681	+	0.285902i	0.706499	−	0.707714i	$-0.250273\pi$
$349$	11.0909	+	5.34109i	0.593681	+	0.285902i	−0.112818	+	0.993616i	$0.535988\pi$
$350$	21.3881	−	2.92756i	1.14324	−	0.156485i
$351$	−0.0694547	+	0.0334476i	−0.00370722	+	0.00178530i
$352$	7.25845	+	18.4942i	0.386876	+	0.985745i
$353$	−0.223186	−	2.97822i	−0.0118790	−	0.158514i	−0.999989	−	0.00476354i	$-0.998484\pi$
$353$	−0.223186	−	2.97822i	−0.0118790	−	0.158514i	0.988110	−	0.153751i	$-0.0491353\pi$
$354$	−0.122693	+	0.312617i	−0.00652107	+	0.0166154i
$355$	7.69135	+	2.37247i	0.408214	+	0.125917i
$356$	−1.68138	−	2.10839i	−0.0891132	−	0.111744i
$357$	−0.0118172	+	0.00347027i	−0.000625434	+	0.000183666i
$358$	−1.11344	+	1.39621i	−0.0588470	+	0.0737918i
$359$	−16.5242	+	11.2660i	−0.872116	+	0.594599i	−0.914537	−	0.404501i	$-0.867445\pi$
$359$	−16.5242	+	11.2660i	−0.872116	+	0.594599i	0.0424215	+	0.999100i	$0.486493\pi$
$360$	−1.99815	+	1.85401i	−0.105312	+	0.0977150i
$361$	6.92802	+	11.9997i	0.364632	+	0.631562i
$362$	−12.4412	+	21.5488i	−0.653895	+	1.13258i
$363$	−0.00358384	−	0.0157018i	−0.000188103	−	0.000824132i
$364$	−3.07000	−	1.53008i	−0.160912	−	0.0801981i
$365$	0.507028	−	2.22144i	0.0265391	−	0.116275i
$366$	0.168141	+	0.156012i	0.00878886	+	0.00815487i
$367$	−18.7125	−	2.82045i	−0.976783	−	0.147226i	−0.358797	−	0.933416i	$-0.616813\pi$
$367$	−18.7125	−	2.82045i	−0.976783	−	0.147226i	−0.617986	+	0.786189i	$0.712051\pi$
$368$	−9.52811	−	1.43613i	−0.496687	−	0.0748635i
$369$	16.3355	+	15.1572i	0.850394	+	0.789050i
$370$	1.32853	−	5.82067i	0.0690670	−	0.302602i
$371$	3.59983	−	1.67381i	0.186894	−	0.0868997i
$372$	−0.0160101	−	0.0701450i	−0.000830088	−	0.00363685i
$373$	−14.2206	+	24.6309i	−0.736317	+	1.27534i	0.217827	+	0.975987i	$0.430103\pi$
$373$	−14.2206	+	24.6309i	−0.736317	+	1.27534i	−0.954143	+	0.299350i	$0.903230\pi$
$374$	1.02682	+	1.77851i	0.0530958	+	0.0919646i
$375$	−0.0636105	+	0.0590220i	−0.00328483	+	0.00304788i
$376$	4.66298	−	3.17917i	0.240475	−	0.163953i
$377$	−2.15760	+	2.70555i	−0.111122	+	0.139343i
$378$	0.0226611	+	0.369616i	0.00116556	+	0.0190110i
$379$	6.43875	+	8.07394i	0.330737	+	0.414731i	0.919199	−	0.393794i	$-0.128838\pi$
$379$	6.43875	+	8.07394i	0.330737	+	0.414731i	−0.588462	+	0.808525i	$0.700266\pi$
$380$	−1.99882	−	0.616555i	−0.102537	−	0.0316286i
$381$	−0.0323743	+	0.0824883i	−0.00165858	+	0.00422600i
$382$	−1.55911	−	20.8048i	−0.0797709	−	1.06447i
$383$	1.72557	+	4.39667i	0.0881723	+	0.224659i	0.968158	−	0.250342i	$-0.0805429\pi$
$383$	1.72557	+	4.39667i	0.0881723	+	0.224659i	−0.879985	+	0.475001i	$0.842448\pi$
$384$	0.110973	−	0.0534418i	0.00566307	−	0.00272719i
$385$	−5.59076	−	1.80794i	−0.284931	−	0.0921412i
$386$	23.3767	+	11.2576i	1.18984	+	0.572999i
$387$	1.52213	−	20.3115i	0.0773744	−	1.03249i
$388$	4.96411	−	1.53122i	0.252014	−	0.0777361i
$389$	−11.9707	−	8.16152i	−0.606941	−	0.413805i	0.220477	−	0.975392i	$-0.429239\pi$
$389$	−11.9707	−	8.16152i	−0.606941	−	0.413805i	−0.827418	+	0.561587i	$0.810191\pi$
$390$	0.0164095	−	0.00247333i	0.000830926	−	0.000125242i
$391$	−0.710712			−0.0359423
$392$	6.71700	−	5.90155i	0.339260	−	0.298073i
$393$	−0.0959230			−0.00483867
$394$	21.1774	−	3.19197i	1.06690	−	0.160809i
$395$	3.07981	+	2.09978i	0.154962	+	0.105651i
$396$	11.6025	−	3.57890i	0.583048	−	0.179846i
$397$	2.04616	−	27.3041i	0.102694	−	1.37035i	−0.673186	−	0.739473i	$-0.735075\pi$
$397$	2.04616	−	27.3041i	0.102694	−	1.37035i	0.775880	−	0.630880i	$-0.217306\pi$
$398$	−23.8128	−	11.4677i	−1.19363	−	0.574822i
$399$	0.0642858	−	0.0425634i	0.00321831	−	0.00213083i
$400$	−19.8887	+	9.57787i	−0.994433	+	0.478894i
$401$	−11.2463	−	28.6551i	−0.561614	−	1.43097i	−0.876296	−	0.481772i	$-0.839993\pi$
$401$	−11.2463	−	28.6551i	−0.561614	−	1.43097i	0.314682	−	0.949197i	$-0.398102\pi$
$402$	0.0179178	+	0.239096i	0.000893657	+	0.0119250i
$403$	−1.57799	+	4.02065i	−0.0786053	+	0.200283i
$404$	0.905065	+	0.279175i	0.0450287	+	0.0138895i
$405$	3.99112	+	5.00471i	0.198320	+	0.248686i
$406$	8.11556	+	14.5076i	0.402769	+	0.720000i
$407$	8.99775	−	11.2828i	0.446002	−	0.559268i
$408$	0.00491287	−	0.00334954i	0.000243223	−	0.000165827i
$409$	15.5846	−	14.4604i	0.770608	−	0.715020i	−0.193334	−	0.981133i	$-0.561930\pi$
$409$	15.5846	−	14.4604i	0.770608	−	0.715020i	0.963942	+	0.266113i	$0.0857396\pi$
$410$	−4.79724	−	8.30906i	−0.236919	−	0.410355i
$411$	0.0143261	−	0.0248135i	0.000706653	−	0.00122396i
$412$	−3.81883	−	16.7314i	−0.188140	−	0.824297i
$413$	−7.97093	−	37.2451i	−0.392224	−	1.83271i
$414$	−2.37745	+	10.4163i	−0.116845	+	0.511932i
$415$	8.67641	+	8.05053i	0.425908	+	0.395185i
$416$	6.29278	+	0.948485i	0.308529	+	0.0465033i
$417$	0.0502952	+	0.00758079i	0.00246297	+	0.000371233i
$418$	−9.42396	−	8.74416i	−0.460941	−	0.427691i
$419$	−6.94435	+	30.4252i	−0.339254	+	1.48637i	0.461374	+	0.887206i	$0.347356\pi$
$419$	−6.94435	+	30.4252i	−0.339254	+	1.48637i	−0.800628	+	0.599162i	$0.795501\pi$
$420$	0.00739045	−	0.0304683i	0.000360617	−	0.00148670i
$421$	1.77664	+	7.78395i	0.0865879	+	0.379366i	0.999591	−	0.0285854i	$-0.00910026\pi$
$421$	1.77664	+	7.78395i	0.0865879	+	0.379366i	−0.913003	+	0.407952i	$0.866243\pi$
$422$	18.4496	−	31.9557i	0.898114	−	1.55558i
$423$	−6.62712	−	11.4785i	−0.322221	−	0.558104i
$424$	−1.40498	+	1.30363i	−0.0682318	+	0.0633099i
$425$	−1.34527	+	0.917192i	−0.0652554	+	0.0444904i
$426$	−0.164570	+	0.206364i	−0.00797344	+	0.00999838i
$427$	−25.6686	−	4.22583i	−1.24219	−	0.204502i
$428$	−5.17803	−	6.49305i	−0.250290	−	0.313853i
$429$	0.0383301	+	0.0118233i	0.00185060	+	0.000570833i
$430$	−3.20390	+	8.16340i	−0.154506	+	0.393674i
$431$	0.429452	+	5.73064i	0.0206860	+	0.276035i	0.997949	+	0.0640067i	$0.0203879\pi$
$431$	0.429452	+	5.73064i	0.0206860	+	0.276035i	−0.977263	+	0.212028i	$0.931993\pi$
$432$	−0.138343	−	0.352492i	−0.00665603	−	0.0169593i
$433$	13.2344	−	6.37337i	0.636007	−	0.306285i	−0.0879553	−	0.996124i	$-0.528033\pi$
$433$	13.2344	−	6.37337i	0.636007	−	0.306285i	0.723962	+	0.689840i	$0.242319\pi$
$434$	15.0167	+	14.3174i	0.720822	+	0.687257i
$435$	−0.0284970	−	0.0137234i	−0.00136633	−	0.000657988i
$436$	−0.285165	+	3.80526i	−0.0136569	+	0.182239i
$437$	4.25138	−	1.31138i	0.203371	−	0.0627317i
$438$	0.0617376	+	0.0420920i	0.00294994	+	0.00201123i
$439$	−23.5284	+	3.54633i	−1.12295	+	0.169257i	−0.684159	−	0.729333i	$-0.739830\pi$
$439$	−23.5284	+	3.54633i	−1.12295	+	0.169257i	−0.438789	+	0.898590i	$0.644592\pi$
$440$	2.83674			0.135237
$441$	−12.6423	−	16.7667i	−0.602016	−	0.798415i
$442$	0.657812			0.0312889
$443$	17.4669	−	2.63271i	0.829878	−	0.125084i	0.279654	−	0.960101i	$-0.409780\pi$
$443$	17.4669	−	2.63271i	0.829878	−	0.125084i	0.550224	+	0.835017i	$0.314542\pi$
$444$	0.0636215	+	0.0433764i	0.00301934	+	0.00205855i
$445$	−1.41394	+	0.436142i	−0.0670271	+	0.0206751i
$446$	0.648179	−	8.64934i	0.0306921	−	0.409558i
$447$	0.222466	+	0.107134i	0.0105223	+	0.00506727i
$448$	2.34237	−	3.93290i	0.110667	−	0.185812i
$449$	−16.0695	+	7.73864i	−0.758365	+	0.365209i	−0.772769	−	0.634687i	$-0.781129\pi$
$449$	−16.0695	+	7.73864i	−0.758365	+	0.365209i	0.0144047	+	0.999896i	$0.495415\pi$
$450$	8.94231	+	22.7846i	0.421545	+	1.07408i
$451$	−1.73309	−	23.1265i	−0.0816080	−	1.08898i
$452$	2.74781	−	7.00129i	0.129246	−	0.329313i
$453$	−0.242399	−	0.0747703i	−0.0113889	−	0.00351301i
$454$	−19.2422	−	24.1290i	−0.903084	−	1.13243i
$455$	−1.39692	+	1.26132i	−0.0654887	+	0.0591317i
$456$	−0.0232077	+	0.0291015i	−0.00108680	+	0.00136280i
$457$	8.14550	−	5.55351i	0.381030	−	0.259782i	−0.357625	−	0.933865i	$-0.616413\pi$
$457$	8.14550	−	5.55351i	0.381030	−	0.259782i	0.738655	+	0.674083i	$0.235461\pi$
$458$	34.8267	−	32.3145i	1.62735	−	1.50996i
$459$	−0.0139649	−	0.0241879i	−0.000651826	−	0.00112900i
$460$	0.904583	−	1.56678i	0.0421764	−	0.0730517i
$461$	3.27261	+	14.3382i	0.152420	+	0.667798i	0.992177	+	0.124835i	$0.0398403\pi$
$461$	3.27261	+	14.3382i	0.152420	+	0.667798i	−0.839757	+	0.542962i	$0.817303\pi$
$462$	0.122171	−	0.149005i	0.00568389	−	0.00693232i
$463$	−7.89671	+	34.5977i	−0.366991	+	1.60789i	0.368007	+	0.929823i	$0.380040\pi$
$463$	−7.89671	+	34.5977i	−0.366991	+	1.60789i	−0.734998	+	0.678070i	$0.762817\pi$
$464$	−12.4607	−	11.5619i	−0.578475	−	0.536747i
$465$	−0.0390369	−	0.00588386i	−0.00181029	−	0.000272858i
$466$	−2.23527	−	0.336913i	−0.103547	−	0.0156072i
$467$	30.1216	+	27.9488i	1.39386	+	1.29331i	0.907808	+	0.419386i	$0.137755\pi$
$467$	30.1216	+	27.9488i	1.39386	+	1.29331i	0.486054	+	0.873929i	$0.338436\pi$
$468$	0.865435	−	3.79172i	0.0400047	−	0.175272i
$469$	−16.6647	−	21.4885i	−0.769503	−	0.992248i
$470$	1.26984	+	5.56352i	0.0585733	+	0.256626i
$471$	−0.0917764	+	0.158961i	−0.00422883	+	0.00732455i
$472$	9.19423	+	15.9249i	0.423199	+	0.733002i
$473$	−15.5389	+	14.4180i	−0.714477	+	0.662938i
$474$	−0.100996	+	0.0688582i	−0.00463892	+	0.00316276i
$475$	6.35488	−	7.96876i	0.291582	−	0.365632i
$476$	0.469688	−	1.15060i	0.0215281	−	0.0527376i
$477$	2.80647	+	3.51921i	0.128500	+	0.161133i
$478$	32.2320	+	9.94227i	1.47426	+	0.454749i
$479$	8.97698	−	22.8730i	0.410169	−	1.04509i	−0.565287	−	0.824895i	$-0.691234\pi$
$479$	8.97698	−	22.8730i	0.410169	−	1.04509i	0.975455	−	0.220198i	$-0.0706704\pi$
$480$	0.00434674	+	0.0580032i	0.000198401	+	0.00264747i
$481$	−1.68880	−	4.30300i	−0.0770027	−	0.196200i
$482$	4.12313	−	1.98560i	0.187803	−	0.0904414i
$483$	0.0235179	+	0.0623988i	0.00107010	+	0.00283924i
$484$	1.46420	+	0.705123i	0.0665547	+	0.0320510i
$485$	0.213011	−	2.84243i	0.00967232	−	0.129068i
$486$	−0.601829	+	0.185640i	−0.0272995	+	0.00842079i
$487$	−22.3279	−	15.2229i	−1.01177	−	0.689815i	−0.0605013	−	0.998168i	$-0.519270\pi$
$487$	−22.3279	−	15.2229i	−1.01177	−	0.689815i	−0.951272	+	0.308353i	$0.900222\pi$
$488$	12.4189	−	1.87185i	0.562178	−	0.0847347i
$489$	−0.212116			−0.00959223
$490$	3.07352	+	8.50258i	0.138847	+	0.384107i
$491$	−6.10285			−0.275418			−0.137709	−	0.990473i	$-0.543974\pi$
$491$	−6.10285			−0.275418			−0.137709	+	0.990473i	$0.543974\pi$
$492$	0.122361	−	0.0184429i	0.00551644	−	0.000831470i
$493$	−1.03591	−	0.706275i	−0.0466552	−	0.0318090i
$494$	−3.93494	+	1.21377i	−0.177041	+	0.0546100i
$495$	0.497866	−	6.64355i	0.0223774	−	0.298606i
$496$	−19.1154	−	9.20548i	−0.858306	−	0.413338i
$497$	2.64189	−	29.8191i	0.118505	−	1.33757i
$498$	−0.349702	+	0.168408i	−0.0156705	+	0.00754652i
$499$	6.38297	+	16.2635i	0.285741	+	0.728056i	0.999614	+	0.0277808i	$0.00884403\pi$
$499$	6.38297	+	16.2635i	0.285741	+	0.728056i	−0.713873	+	0.700275i	$0.753061\pi$
$500$	−0.654340	−	8.73157i	−0.0292630	−	0.390488i
$501$	−0.0677069	+	0.172514i	−0.00302492	+	0.00770737i
$502$	−10.3754	−	3.20039i	−0.463077	−	0.142840i
$503$	−10.2401	−	12.8407i	−0.456585	−	0.572540i	0.499244	−	0.866461i	$-0.333611\pi$
$503$	−10.2401	−	12.8407i	−0.456585	−	0.572540i	−0.955830	+	0.293921i	$0.905040\pi$
$504$	8.29807	+	5.82399i	0.369625	+	0.259421i
$505$	0.324022	−	0.406310i	0.0144188	−	0.0180806i
$506$	9.18698	−	6.26357i	0.408411	−	0.278450i
$507$	0.00941861	−	0.00873920i	0.000418295	−	0.000388121i
$508$	−4.47080	−	7.74366i	−0.198360	−	0.343569i
$509$	9.62493	−	16.6709i	0.426617	−	0.738923i	−0.569953	−	0.821678i	$-0.693038\pi$
$509$	9.62493	−	16.6709i	0.426617	−	0.738923i	0.996570	+	0.0827545i	$0.0263717\pi$
$510$	0.00133789	+	0.00586167i	5.92427e−5	+	0.000259559i
$511$	−8.47375	−	0.114969i	−0.374857	−	0.00508591i
$512$	−4.16364	+	18.2421i	−0.184009	+	0.806195i
$513$	0.128167	+	0.118921i	0.00565870	+	0.00525051i
$514$	−11.9260	−	1.79756i	−0.526035	−	0.0792871i
$515$	−9.31131	−	1.40345i	−0.410305	−	0.0618436i
$516$	−0.0829112	−	0.0769304i	−0.00364996	−	0.00338667i
$517$	−3.06939	+	13.4479i	−0.134992	+	0.591437i
$518$	−22.2031	−	0.301244i	−0.975550	−	0.0132359i
$519$	0.00779690	+	0.0341605i	0.000342246	+	0.00149948i
$520$	0.454324	−	0.786913i	0.0199234	−	0.0345084i
$521$	2.61474	+	4.52886i	0.114554	+	0.198413i	0.917601	−	0.397502i	$-0.130123\pi$
$521$	2.61474	+	4.52886i	0.114554	+	0.198413i	−0.803048	+	0.595915i	$0.796790\pi$
$522$	−13.8165	+	12.8199i	−0.604733	+	0.561111i
$523$	−1.75386	+	1.19576i	−0.0766910	+	0.0522870i	−0.601059	−	0.799205i	$-0.705254\pi$
$523$	−1.75386	+	1.19576i	−0.0766910	+	0.0522870i	0.524368	+	0.851492i	$0.324302\pi$
$524$	6.03484	−	7.56745i	0.263633	−	0.330586i
$525$	0.125043	+	0.0877612i	0.00545733	+	0.00383021i
$526$	−24.9983	−	31.3469i	−1.08998	−	1.36679i
$527$	−1.49536	−	0.461258i	−0.0651390	−	0.0200927i
$528$	−0.0719850	+	0.183415i	−0.00313275	+	0.00798211i
$529$	−1.43123	−	19.0984i	−0.0622274	−	0.830367i
$530$	−0.708032	−	1.80404i	−0.0307549	−	0.0783623i
$531$	38.9091	−	18.7376i	1.68851	−	0.813145i
$532$	−0.686574	+	7.74937i	−0.0297667	+	0.335978i
$533$	−6.69285	−	3.22311i	−0.289899	−	0.139608i
$534$	0.00362614	−	0.0483875i	0.000156918	−	0.00209393i
$535$	−4.35440	+	1.34315i	−0.188257	+	0.0580696i
$536$	10.8472	+	7.39549i	0.468528	+	0.319437i
$537$	−0.0124964	+	0.00188353i	−0.000539260	+	8.12804e-5i
$538$	9.68412			0.417512
$539$	−2.22375	+	21.7401i	−0.0957838	+	0.936414i
$540$	0.0710972			0.00305954
$541$	−38.5640	+	5.81258i	−1.65799	+	0.249903i	−0.910243	−	0.414075i	$-0.864105\pi$
$541$	−38.5640	+	5.81258i	−1.65799	+	0.249903i	−0.747752	+	0.663978i	$0.768867\pi$
$542$	−25.1172	−	17.1246i	−1.07888	−	0.735566i
$543$	−0.168261	+	0.0519016i	−0.00722077	+	0.00222731i
$544$	−0.172303	+	2.29922i	−0.00738743	+	0.0985784i
$545$	1.88642	+	0.908454i	0.0808055	+	0.0389139i
$546$	−0.0217674	−	0.0577542i	−0.000931557	−	0.00247165i
$547$	−20.3053	+	9.77851i	−0.868192	+	0.418099i	−0.814298	−	0.580448i	$-0.802878\pi$
$547$	−20.3053	+	9.77851i	−0.868192	+	0.418099i	−0.0538941	+	0.998547i	$0.517163\pi$
$548$	1.05626	+	2.69130i	0.0451210	+	0.114966i
$549$	−2.20421	−	29.4132i	−0.0940735	−	1.25532i
$550$	9.30629	−	23.7120i	0.396822	−	1.01108i
$551$	7.49989	+	2.31341i	0.319506	+	0.0985546i
$552$	−0.0200724	−	0.0251700i	−0.000854340	−	0.00107131i
$553$	5.23950	−	12.8352i	0.222806	−	0.545810i
$554$	28.9477	−	36.2992i	1.22987	−	1.54221i
$555$	0.0349086	−	0.0238003i	0.00148179	−	0.00101027i
$556$	−3.76230	+	3.49090i	−0.159557	+	0.148047i
$557$	−9.53076	−	16.5078i	−0.403831	−	0.699456i	0.590353	−	0.807145i	$-0.298988\pi$
$557$	−9.53076	−	16.5078i	−0.403831	−	0.699456i	−0.994185	+	0.107689i	$0.965655\pi$
$558$	−11.7625	+	20.3732i	−0.497945	+	0.862466i
$559$	1.51088	+	6.61961i	0.0639036	+	0.279980i
$560$	−5.66563	−	7.30564i	−0.239417	−	0.308719i
$561$	−0.00323388	+	0.0141686i	−0.000136535	+	0.000598197i
$562$	−18.2364	−	16.9209i	−0.769254	−	0.713763i
$563$	29.5674	+	4.45656i	1.24612	+	0.187822i	0.738792	−	0.673934i	$-0.235397\pi$
$563$	29.5674	+	4.45656i	1.24612	+	0.187822i	0.507324	+	0.861755i	$0.330635\pi$
$564$	−0.0727776	−	0.0109695i	−0.00306449	−	0.000461898i
$565$	−3.02518	−	2.80696i	−0.127270	−	0.118089i
$566$	−10.1811	+	44.6065i	−0.427945	+	1.87495i
$567$	15.0951	−	18.4106i	0.633934	−	0.773173i
$568$	3.21600	+	14.0902i	0.134940	+	0.591212i
$569$	6.92108	−	11.9877i	0.290147	−	0.502549i	−0.683698	−	0.729765i	$-0.739629\pi$
$569$	6.92108	−	11.9877i	0.290147	−	0.502549i	0.973844	+	0.227217i	$0.0729626\pi$
$570$	−0.0188188	−	0.0325951i	−0.000788232	−	0.00136526i
$571$	−19.5593	+	18.1484i	−0.818533	+	0.759488i	−0.973562	−	0.228422i	$-0.926643\pi$
$571$	−19.5593	+	18.1484i	−0.818533	+	0.759488i	0.155029	+	0.987910i	$0.450453\pi$
$572$	−3.34423	+	2.28006i	−0.139829	+	0.0953340i
$573$	0.0920527	−	0.115430i	0.00384556	−	0.00482218i
$574$	−26.4852	+	23.9143i	−1.10547	+	0.998163i
$575$	5.49636	+	6.89222i	0.229214	+	0.287426i
$576$	4.95964	+	1.52985i	0.206652	+	0.0637436i
$577$	10.9066	−	27.7895i	0.454047	−	1.15689i	−0.502308	−	0.864689i	$-0.667516\pi$
$577$	10.9066	−	27.7895i	0.454047	−	1.15689i	0.956356	−	0.292205i	$-0.0943891\pi$
$578$	−2.28878	−	30.5416i	−0.0952005	−	1.27036i
$579$	0.0670810	+	0.170920i	0.00278779	+	0.00710317i
$580$	2.87550	−	1.38477i	0.119398	−	0.0574993i
$581$	22.5257	−	37.8212i	0.934522	−	1.56909i
$582$	0.0842167	+	0.0405566i	0.00349090	+	0.00168113i
$583$	0.350069	−	4.67135i	0.0144984	−	0.193468i
$584$	3.90959	−	1.20595i	0.161780	−	0.0499025i
$585$	−1.76318	−	1.20212i	−0.0728987	−	0.0497015i
$586$	−49.9626	+	7.53065i	−2.06393	+	0.311088i
$587$	45.7642			1.88889			0.944445	−	0.328670i	$-0.106600\pi$
$587$	45.7642			1.88889			0.944445	+	0.328670i	$0.106600\pi$
$588$	−0.116562	−	0.00316352i	−0.00480693	−	0.000130461i
$589$	9.79614			0.403643
$590$	−18.3860	+	2.77124i	−0.756938	+	0.114090i
$591$	0.125223	+	0.0853753i	0.00515097	+	0.00351187i
$592$	21.6976	−	6.69281i	0.891764	−	0.275073i
$593$	−3.45043	+	46.0428i	−0.141692	+	1.89075i	0.246454	+	0.969154i	$0.420735\pi$
$593$	−3.45043	+	46.0428i	−0.141692	+	1.89075i	−0.388146	+	0.921598i	$0.626885\pi$
$594$	0.393687	+	0.189590i	0.0161532	+	0.00777896i
$595$	−0.493530	−	0.470548i	−0.0202327	−	0.0192906i
$596$	−22.4480	+	10.8104i	−0.919507	+	0.442811i
$597$	−0.0683324	−	0.174108i	−0.00279666	−	0.00712577i
$598$	−0.266157	−	3.55162i	−0.0108840	−	0.145237i
$599$	−5.03372	+	12.8257i	−0.205672	+	0.524045i	−0.996072	−	0.0885469i	$-0.971778\pi$
$599$	−5.03372	+	12.8257i	−0.205672	+	0.524045i	0.790400	+	0.612592i	$0.209873\pi$
$600$	−0.0704767	−	0.0217392i	−0.00287720	−	0.000887499i
$601$	−1.86649	−	2.34050i	−0.0761356	−	0.0954711i	0.742305	−	0.670062i	$-0.233733\pi$
$601$	−1.86649	−	2.34050i	−0.0761356	−	0.0954711i	−0.818441	+	0.574591i	$0.805161\pi$
$602$	32.1831	+	5.29830i	1.31168	+	0.215943i
$603$	19.2237	−	24.1058i	0.782851	−	0.981664i
$604$	21.1489	−	14.4190i	0.860535	−	0.586703i
$605$	0.653664	−	0.606512i	0.0265752	−	0.0246582i
$606$	0.00852113	+	0.0147590i	0.000346147	+	0.000599545i
$607$	−6.09787	+	10.5618i	−0.247505	+	0.428691i	−0.962833	−	0.270098i	$-0.912944\pi$
$607$	−6.09787	+	10.5618i	−0.247505	+	0.428691i	0.715328	+	0.698789i	$0.246277\pi$
$608$	−3.21174	−	14.0716i	−0.130253	−	0.570678i
$609$	−0.0277301	+	0.114322i	−0.00112368	+	0.00463255i
$610$	−2.82587	+	12.3809i	−0.114416	+	0.501289i
$611$	3.23886	+	3.00522i	0.131030	+	0.121578i
$612$	1.39336	+	0.210015i	0.0563231	+	0.00848934i
$613$	−26.1908	−	3.94762i	−1.05784	−	0.159443i	−0.402989	−	0.915205i	$-0.632029\pi$
$613$	−26.1908	−	3.94762i	−1.05784	−	0.159443i	−0.654846	+	0.755762i	$0.727267\pi$
$614$	26.6444	+	24.7224i	1.07528	+	0.997715i
$615$	0.0151084	−	0.0661944i	0.000609231	−	0.00266921i
$616$	−2.20795	−	10.3169i	−0.0889610	−	0.415680i
$617$	−5.46537	−	23.9454i	−0.220028	−	0.964004i	−0.957456	−	0.288579i	$-0.906817\pi$
$617$	−5.46537	−	23.9454i	−0.220028	−	0.964004i	0.737428	−	0.675425i	$-0.236040\pi$
$618$	0.154398	−	0.267425i	0.00621079	−	0.0107574i
$619$	−9.09923	−	15.7603i	−0.365729	−	0.633461i	0.623164	−	0.782091i	$-0.285847\pi$
$619$	−9.09923	−	15.7603i	−0.365729	−	0.633461i	−0.988893	+	0.148630i	$0.952514\pi$
$620$	2.92013	−	2.70948i	0.117275	−	0.108815i
$621$	−0.124944	+	0.0851852i	−0.00501382	+	0.00341837i
$622$	−18.5280	+	23.2334i	−0.742906	+	0.931575i
$623$	2.68672	+	4.80286i	0.107641	+	0.192422i
$624$	0.0393504	+	0.0493438i	0.00157528	+	0.00197533i
$625$	16.8806	+	5.20697i	0.675223	+	0.208279i
$626$	−7.70440	+	19.6305i	−0.307930	+	0.784593i
$627$	−0.00679863	−	0.0907214i	−0.000271511	−	0.00362306i
$628$	−6.76664	−	17.2411i	−0.270018	−	0.687996i
$629$	1.50892	−	0.726658i	0.0601646	−	0.0289737i
$630$	−8.54734	+	5.65916i	−0.340534	+	0.225466i
$631$	1.24042	+	0.597357i	0.0493805	+	0.0237804i	0.458411	−	0.888740i	$-0.348419\pi$
$631$	1.24042	+	0.597357i	0.0493805	+	0.0237804i	−0.409031	+	0.912521i	$0.634133\pi$
$632$	−0.500172	+	6.67433i	−0.0198958	+	0.265491i
$633$	0.249522	−	0.0769673i	0.00991760	−	0.00305917i
$634$	6.08992	+	4.15204i	0.241862	+	0.164899i
$635$	−4.85139	+	0.731229i	−0.192522	+	0.0290180i
$636$	0.0249950			0.000991115
$637$	5.67456	+	4.09870i	0.224834	+	0.162396i
$638$	19.6151			0.776571
$639$	33.5632	−	5.05883i	1.32774	−	0.200124i
$640$	5.63451	+	3.84154i	0.222723	+	0.151850i
$641$	−46.4064	+	14.3145i	−1.83294	+	0.565387i	−0.833014	+	0.553251i	$0.813387\pi$
$641$	−46.4064	+	14.3145i	−1.83294	+	0.565387i	−0.999926	+	0.0121362i	$0.996137\pi$
$642$	0.0111671	−	0.149015i	0.000440732	−	0.00588116i
$643$	24.2047	+	11.6564i	0.954541	+	0.459683i	0.845276	−	0.534330i	$-0.179436\pi$
$643$	24.2047	+	11.6564i	0.954541	+	0.459683i	0.109265	+	0.994013i	$0.465150\pi$
$644$	−6.40229	−	2.07037i	−0.252285	−	0.0815841i
$645$	−0.0559136	+	0.0269265i	−0.00220159	+	0.00106023i
$646$	−0.545066	−	1.38881i	−0.0214453	−	0.0546419i
$647$	−0.399591	−	5.33218i	−0.0157096	−	0.209630i	−0.999535	−	0.0304986i	$-0.990290\pi$
$647$	−0.399591	−	5.33218i	−0.0157096	−	0.209630i	0.983825	−	0.179131i	$-0.0573286\pi$
$648$	−4.19924	+	10.6995i	−0.164962	+	0.420315i
$649$	−42.9470	−	13.2474i	−1.68582	−	0.520005i
$650$	−5.08725	−	6.37921i	−0.199538	−	0.250213i
$651$	0.00898508	+	0.146552i	0.000352153	+	0.00574384i
$652$	13.3450	−	16.7341i	0.522629	−	0.655356i
$653$	−4.54911	+	3.10153i	−0.178021	+	0.121372i	−0.649052	−	0.760744i	$-0.724834\pi$
$653$	−4.54911	+	3.10153i	−0.178021	+	0.121372i	0.471031	+	0.882116i	$0.343882\pi$
$654$	−0.0503323	+	0.0467016i	−0.00196815	+	0.00182618i
$655$	−2.65543	−	4.59934i	−0.103756	−	0.179711i
$656$	18.2448	−	31.6009i	0.712339	−	1.23381i
$657$	−2.13813	−	9.36777i	−0.0834165	−	0.365472i
$658$	19.2455	−	8.94857i	0.750269	−	0.348852i
$659$	−11.2587	+	49.3278i	−0.438579	+	1.92154i	−0.0537389	+	0.998555i	$0.517114\pi$
$659$	−11.2587	+	49.3278i	−0.438579	+	1.92154i	−0.384840	+	0.922983i	$0.625743\pi$
$660$	−0.0271189	−	0.0251627i	−0.00105560	−	0.000979456i
$661$	43.0798	+	6.49324i	1.67561	+	0.252558i	0.916971	−	0.398954i	$-0.130627\pi$
$661$	43.0798	+	6.49324i	1.67561	+	0.252558i	0.758639	+	0.651511i	$0.225865\pi$
$662$	−2.50995	−	0.378313i	−0.0975518	−	0.0147036i
$663$	0.00341243	+	0.00316627i	0.000132528	+	0.000122968i
$664$	−4.72914	+	20.7197i	−0.183526	+	0.804082i
$665$	3.82046	+	1.90411i	0.148151	+	0.0738384i
$666$	−5.60239	−	24.5457i	−0.217088	−	0.951126i
$667$	−3.39414	+	5.87882i	−0.131422	+	0.227629i
$668$	−9.35014	−	16.1949i	−0.361768	−	0.626600i
$669$	0.0449946	−	0.0417489i	0.00173959	−	0.00161411i
$670$	−10.9682	+	7.47801i	−0.423740	+	0.288901i
$671$	−19.1388	+	23.9993i	−0.738844	+	0.926482i
$672$	0.207568	−	0.0609549i	0.00800710	−	0.00235138i
$673$	19.5863	+	24.5604i	0.754995	+	0.946734i	0.999739	−	0.0228536i	$-0.00727515\pi$
$673$	19.5863	+	24.5604i	0.754995	+	0.946734i	−0.244743	+	0.969588i	$0.578704\pi$
$674$	13.5875	+	4.19118i	0.523370	+	0.161438i
$675$	−0.126566	+	0.322486i	−0.00487155	+	0.0124125i
$676$	0.0968862	+	1.29286i	0.00372639	+	0.0497252i
$677$	0.301187	+	0.767412i	0.0115756	+	0.0294940i	0.936545	−	0.350548i	$-0.114005\pi$
$677$	0.301187	+	0.767412i	0.0115756	+	0.0294940i	−0.924969	+	0.380042i	$0.875909\pi$
$678$	0.121929	−	0.0587181i	0.00468267	−	0.00225506i
$679$	−10.5034	+	1.43768i	−0.403083	+	0.0551733i
$680$	0.296608	+	0.142839i	0.0113744	+	0.00547761i
$681$	0.0163211	−	0.217790i	0.000625425	−	0.00834572i
$682$	23.3948	−	7.21634i	0.895833	−	0.276328i
$683$	−37.3270	−	25.4491i	−1.42828	−	0.973783i	−0.997452	−	0.0713471i	$-0.977270\pi$
$683$	−37.3270	−	25.4491i	−1.42828	−	0.973783i	−0.430825	−	0.902435i	$-0.641777\pi$
$684$	−8.72237	+	1.31469i	−0.333508	+	0.0502683i
$685$	1.58635			0.0606114
$686$	28.5307	−	17.7959i	1.08931	−	0.679452i
$687$	0.336205			0.0128270
$688$	−32.9799	+	4.97092i	−1.25735	+	0.189514i
$689$	−1.23977	−	0.845258i	−0.0472313	−	0.0322018i
$690$	0.0311067	−	0.00959514i	0.00118421	−	0.000365281i
$691$	2.63669	−	35.1842i	0.100304	−	1.33847i	−0.689131	−	0.724637i	$-0.742008\pi$
$691$	2.63669	−	35.1842i	0.100304	−	1.33847i	0.789436	−	0.613833i	$-0.210373\pi$
$692$	−3.18548	−	1.53405i	−0.121094	−	0.0583157i
$693$	−24.5493	+	3.36027i	−0.932553	+	0.127646i
$694$	9.15570	−	4.40915i	0.347546	−	0.167369i
$695$	1.02884	+	2.62143i	0.0390260	+	0.0994365i
$696$	−0.00424415	−	0.0566343i	−0.000160874	−	0.00214672i
$697$	0.983278	−	2.50535i	0.0372443	−	0.0948969i
$698$	−21.3572	−	6.58784i	−0.808384	−	0.249353i
$699$	−0.00997388	−	0.0125069i	−0.000377247	−	0.000473053i
$700$	−14.7905	+	4.34340i	−0.559026	+	0.164165i
$701$	23.7538	−	29.7863i	0.897169	−	1.12501i	−0.0944128	−	0.995533i	$-0.530097\pi$
$701$	23.7538	−	29.7863i	0.897169	−	1.12501i	0.991582	−	0.129481i	$-0.0413312\pi$
$702$	0.115644	−	0.0788446i	0.00436469	−	0.00297580i
$703$	−7.68536	+	7.13097i	−0.289859	+	0.268950i
$704$	−2.70074	−	4.67782i	−0.101788	−	0.176302i
$705$	−0.0201918	+	0.0349732i	−0.000760466	+	0.00131717i
$706$	1.20661	+	5.28652i	0.0454115	+	0.198961i
$707$	−1.72990	−	0.862181i	−0.0650597	−	0.0324257i
$708$	0.0533622	−	0.233795i	0.00200547	−	0.00878656i
$709$	15.1222	+	14.0314i	0.567927	+	0.526959i	0.911031	−	0.412338i	$-0.135288\pi$
$709$	15.1222	+	14.0314i	0.567927	+	0.526959i	−0.343104	+	0.939297i	$0.611478\pi$
$710$	−14.4506	−	2.17808i	−0.542321	−	0.0817418i
$711$	15.5433	+	2.34277i	0.582918	+	0.0878607i
$712$	−1.94763	−	1.80714i	−0.0729907	−	0.0677254i
$713$	−1.88536	+	8.26030i	−0.0706073	+	0.309351i
$714$	0.0202769	−	0.00942812i	0.000758843	−	0.000352839i
$715$	0.494186	+	2.16517i	0.0184815	+	0.0809727i
$716$	0.637598	−	1.10435i	0.0238282	−	0.0412716i
$717$	0.119350	+	0.206720i	0.00445719	+	0.00772009i
$718$	26.6180	−	24.6979i	0.993376	−	0.921718i
$719$	−33.7979	+	23.0430i	−1.26045	+	0.859359i	−0.994511	−	0.104631i	$-0.966634\pi$
$719$	−33.7979	+	23.0430i	−1.26045	+	0.859359i	−0.265938	+	0.963990i	$0.585682\pi$
$720$	6.53565	−	8.19545i	0.243569	−	0.305426i
$721$	2.14317	+	34.9565i	0.0798159	+	1.30185i
$722$	−15.6853	−	19.6688i	−0.583747	−	0.731996i
$723$	0.0309463	+	0.00954566i	0.00115090	+	0.000355007i
$724$	6.49130	−	16.5396i	0.241247	−	0.614688i
$725$	1.16216	+	15.5080i	0.0431616	+	0.575951i
$726$	0.0106832	+	0.0272203i	0.000396491	+	0.00101024i
$727$	−27.2085	+	13.1029i	−1.00911	+	0.485961i	−0.864020	−	0.503458i	$-0.832061\pi$
$727$	−27.2085	+	13.1029i	−1.00911	+	0.485961i	−0.145088	+	0.989419i	$0.546347\pi$
$728$	−3.21553	−	1.03984i	−0.119175	−	0.0385390i
$729$	24.3181	+	11.7110i	0.900671	+	0.433740i
$730$	−0.309159	+	4.12544i	−0.0114425	+	0.152689i
$731$	−2.35072	+	0.725100i	−0.0869444	+	0.0268188i
$732$	−0.135327	−	0.0922644i	−0.00500183	−	0.00341019i
$733$	2.95113	−	0.444811i	0.109002	−	0.0164295i	−0.0943145	−	0.995542i	$-0.530066\pi$
$733$	2.95113	−	0.444811i	0.109002	−	0.0164295i	0.203317	+	0.979113i	$0.434828\pi$
$734$	34.3585			1.26820
$735$	−0.0249818	+	0.0589014i	−0.000921467	+	0.00217261i
$736$	12.4836			0.460150
$737$	−31.7291	+	4.78239i	−1.16875	+	0.176161i
$738$	−33.4295	−	22.7918i	−1.23056	−	0.838979i
$739$	40.6925	−	12.5520i	1.49690	−	0.461732i	0.565196	−	0.824957i	$-0.308801\pi$
$739$	40.6925	−	12.5520i	1.49690	−	0.461732i	0.931701	+	0.363225i	$0.118324\pi$
$740$	−0.318593	+	4.25133i	−0.0117117	+	0.156282i
$741$	−0.0262550	−	0.0126437i	−0.000964500	−	0.000464479i
$742$	−6.00998	+	3.97919i	−0.220633	+	0.146081i
$743$	−38.2670	+	18.4284i	−1.40388	+	0.676073i	−0.973945	−	0.226786i	$-0.927178\pi$
$743$	−38.2670	+	18.4284i	−1.40388	+	0.676073i	−0.429936	+	0.902859i	$0.641464\pi$
$744$	−0.0258975	−	0.0659858i	−0.000949448	−	0.00241916i
$745$	1.02163	+	13.6327i	0.0374295	+	0.499462i
$746$	18.8657	−	48.0690i	0.690722	−	1.75993i
$747$	47.6949	+	14.7119i	1.74506	+	0.538281i
$748$	−0.914316	−	1.14652i	−0.0334307	−	0.0419208i
$749$	8.27410	+	14.7910i	0.302329	+	0.540451i
$750$	0.0982311	−	0.123178i	0.00358689	−	0.00449782i
$751$	8.16984	−	5.57010i	0.298122	−	0.203256i	−0.405016	−	0.914310i	$-0.632734\pi$
$751$	8.16984	−	5.57010i	0.298122	−	0.203256i	0.703138	+	0.711054i	$0.251782\pi$
$752$	−15.9096	+	14.7619i	−0.580163	+	0.538313i
$753$	−0.0384183	−	0.0665424i	−0.00140004	−	0.00242494i
$754$	3.14150	−	5.44124i	0.114407	−	0.198158i
$755$	−3.12522	−	13.6925i	−0.113738	−	0.498321i
$756$	−0.0553379	−	0.258572i	−0.00201262	−	0.00940419i
$757$	−5.06878	+	22.2078i	−0.184228	+	0.807156i	0.795359	+	0.606138i	$0.207282\pi$
$757$	−5.06878	+	22.2078i	−0.184228	+	0.807156i	−0.979588	+	0.201018i	$0.935575\pi$
$758$	−13.7446	−	12.7531i	−0.499227	−	0.463215i
$759$	0.0778065	+	0.0117274i	0.00282420	+	0.000425679i
$760$	−2.03783	−	0.307153i	−0.0739197	−	0.0111416i
$761$	−8.55558	−	7.93842i	−0.310139	−	0.287767i	0.509710	−	0.860346i	$-0.329753\pi$
$761$	−8.55558	−	7.93842i	−0.310139	−	0.287767i	−0.819850	+	0.572579i	$0.805943\pi$
$762$	0.0358012	−	0.156855i	0.00129694	−	0.00568227i
$763$	1.83566	−	7.56779i	0.0664554	−	0.273972i
$764$	3.31507	+	14.5243i	0.119935	+	0.525469i
$765$	0.386579	−	0.669575i	0.0139768	−	0.0242085i
$766$	−4.28774	−	7.42658i	−0.154922	−	0.268333i
$767$	−10.5531	+	9.79182i	−0.381049	+	0.353562i
$768$	−0.221508	+	0.151021i	−0.00799297	+	0.00544951i
$769$	−27.0487	+	33.9180i	−0.975402	+	1.22312i	−0.000610478		1.00000i	$0.500194\pi$
$769$	−27.0487	+	33.9180i	−0.975402	+	1.22312i	−0.974792	+	0.223116i	$0.928377\pi$
$770$	10.5266	+	1.73299i	0.379351	+	0.0624526i
$771$	−0.0532146	−	0.0667290i	−0.00191648	−	0.00240319i
$772$	−17.7043	−	5.46105i	−0.637192	−	0.196548i
$773$	−0.846412	+	2.15662i	−0.0304433	+	0.0775683i	−0.945287	−	0.326240i	$-0.894218\pi$
$773$	−0.846412	+	2.15662i	−0.0304433	+	0.0775683i	0.914844	+	0.403808i	$0.132314\pi$
$774$	2.76362	+	36.8779i	0.0993363	+	1.32555i
$775$	7.09142	+	18.0686i	0.254731	+	0.649045i
$776$	4.61128	−	2.22068i	0.165535	−	0.0797177i
$777$	−0.113730	−	0.108434i	−0.00408003	−	0.00389004i
$778$	23.7001	+	11.4134i	0.849691	+	0.409190i
$779$	−1.25906	+	16.8010i	−0.0451105	+	0.601957i
$780$	−0.0113234	+	0.00349281i	−0.000405443	+	0.000125063i
$781$	−29.1859	−	19.8986i	−1.04435	−	0.712029i
$782$	1.27597	−	0.192322i	0.0456287	−	0.00687742i
$783$	−0.266768			−0.00953351
$784$	−22.1600	+	26.2915i	−0.791427	+	0.938982i
$785$	−10.1626			−0.362718
$786$	0.172215	−	0.0259572i	0.00614269	−	0.000925861i
$787$	44.7083	+	30.4816i	1.59368	+	1.08655i	0.945772	+	0.324832i	$0.105308\pi$
$787$	44.7083	+	30.4816i	1.59368	+	1.08655i	0.647907	+	0.761719i	$0.275645\pi$
$788$	−14.6135	+	4.50767i	−0.520585	+	0.160579i
$789$	0.0212033	−	0.282939i	0.000754858	−	0.0100729i
$790$	−6.09751	−	2.93641i	−0.216940	−	0.104473i
$791$	−7.85395	+	13.1870i	−0.279254	+	0.468875i
$792$	10.7779	−	5.19034i	0.382975	−	0.184431i
$793$	3.59219	+	9.15275i	0.127562	+	0.325024i
$794$	3.71505	+	49.5739i	0.131842	+	1.75931i
$795$	0.00501049	−	0.0127665i	0.000177704	−	0.000452782i
$796$	18.0346	+	5.56293i	0.639219	+	0.197173i
$797$	−9.36197	−	11.7395i	−0.331618	−	0.415836i	0.587869	−	0.808956i	$-0.299967\pi$
$797$	−9.36197	−	11.7395i	−0.331618	−	0.415836i	−0.919487	+	0.393120i	$0.871396\pi$
$798$	−0.103897	+	0.0938118i	−0.00367792	+	0.00332090i
$799$	−0.998075	+	1.25155i	−0.0353093	+	0.0442765i
$800$	23.6295	−	16.1103i	0.835430	−	0.569587i
$801$	−4.57408	+	4.24412i	−0.161617	+	0.149959i
$802$	27.9452	+	48.4025i	0.986779	+	1.70915i
$803$	−4.99989	+	8.66007i	−0.176442	+	0.305607i
$804$	−0.0380978	−	0.166917i	−0.00134361	−	0.00588673i
$805$	−2.34087	+	2.85503i	−0.0825048	+	0.100626i
$806$	1.74503	−	7.64546i	0.0614660	−	0.269300i
$807$	0.0502368	+	0.0466129i	0.00176842	+	0.00164085i
$808$	0.922726	+	0.139079i	0.0324614	+	0.00489277i
$809$	35.9068	+	5.41208i	1.26242	+	0.190278i	0.745934	−	0.666020i	$-0.232003\pi$
$809$	35.9068	+	5.41208i	1.26242	+	0.190278i	0.516481	+	0.856298i	$0.327242\pi$
$810$	−8.51973	−	7.90515i	−0.299353	−	0.277759i
$811$	0.167637	−	0.734466i	0.00588653	−	0.0257906i	−0.971899	−	0.235397i	$-0.924361\pi$
$811$	0.167637	−	0.734466i	0.00588653	−	0.0257906i	0.977786	+	0.209606i	$0.0672182\pi$
$812$	−7.27435	−	9.38003i	−0.255280	−	0.329174i
$813$	−0.0478701	−	0.209732i	−0.00167888	−	0.00735564i
$814$	−13.1009	+	22.6913i	−0.459185	+	0.795331i
$815$	−5.87201	−	10.1706i	−0.205687	−	0.356261i
$816$	−0.0167622	+	0.0155530i	−0.000586794	+	0.000544465i
$817$	12.7237	−	8.67490i	0.445147	−	0.303496i
$818$	−24.0666	+	30.1786i	−0.841469	+	1.05517i
$819$	−2.99961	+	7.34816i	−0.104815	+	0.256765i
$820$	4.27161	+	5.35643i	0.149171	+	0.187055i
$821$	33.2829	+	10.2664i	1.16158	+	0.358300i	0.814854	−	0.579666i	$-0.196817\pi$
$821$	33.2829	+	10.2664i	1.16158	+	0.358300i	0.346727	+	0.937966i	$0.387293\pi$
$822$	−0.0190056	+	0.0484254i	−0.000662895	+	0.00168903i
$823$	−2.72018	−	36.2982i	−0.0948194	−	1.26528i	−0.818243	−	0.574872i	$-0.805052\pi$
$823$	−2.72018	−	36.2982i	−0.0948194	−	1.26528i	0.723424	−	0.690404i	$-0.242567\pi$
$824$	−6.17722	−	15.7393i	−0.215194	−	0.548305i
$825$	0.162411	−	0.0782129i	0.00565442	−	0.00272302i
$826$	24.3892	+	64.7107i	0.848610	+	2.25157i
$827$	29.2896	+	14.1051i	1.01850	+	0.490483i	0.867176	−	0.498001i	$-0.165932\pi$
$827$	29.2896	+	14.1051i	1.01850	+	0.490483i	0.151323	+	0.988484i	$0.451647\pi$
$828$	0.570133	−	7.60790i	0.0198135	−	0.264393i
$829$	16.0671	−	4.95604i	0.558032	−	0.172130i	−0.00289404	−	0.999996i	$-0.500921\pi$
$829$	16.0671	−	4.95604i	0.558032	−	0.172130i	0.560927	+	0.827866i	$0.310445\pi$
$830$	−17.7556	−	12.1056i	−0.616307	−	0.420191i
$831$	0.324888	−	0.0489689i	0.0112702	−	0.00169871i
$832$	−1.73017			−0.0599828
$833$	−1.32719	+	2.16116i	−0.0459846	+	0.0748796i
$834$	−0.0923486			−0.00319777
$835$	−10.1461	+	1.52928i	−0.351120	+	0.0529228i
$836$	7.58482	+	5.17124i	0.262326	+	0.178851i
$837$	−0.318172	+	0.0981429i	−0.0109976	+	0.00339232i
$838$	4.23430	−	56.5028i	0.146271	−	1.95186i
$839$	4.60046	+	2.21547i	0.158826	+	0.0764864i	0.511608	−	0.859219i	$-0.329050\pi$
$839$	4.60046	+	2.21547i	0.158826	+	0.0764864i	−0.352782	+	0.935705i	$0.614764\pi$
$840$	0.00272596	−	0.0307680i	9.40547e−5	−	0.00106160i
$841$	15.3388	−	7.38677i	0.528924	−	0.254716i
$842$	−5.29604	−	13.4941i	−0.182514	−	0.465037i
$843$	−0.0131561	−	0.175555i	−0.000453119	−	0.00604645i
$844$	−9.62625	+	24.5273i	−0.331349	+	0.844264i
$845$	0.679765	+	0.209680i	0.0233846	+	0.00721320i
$846$	15.0041	+	18.8145i	0.515851	+	0.646856i
$847$	−2.71459	−	1.90523i	−0.0932743	−	0.0654644i
$848$	4.59548	−	5.76255i	0.157809	−	0.197887i
$849$	−0.267521	+	0.182393i	−0.00918130	+	0.00625971i
$850$	2.16703	−	2.01071i	0.0743285	−	0.0689668i
$851$	−4.53385	−	7.85287i	−0.155419	−	0.269193i
$852$	0.0942393	−	0.163227i	0.00322859	−	0.00559207i
$853$	−2.23742	−	9.80279i	−0.0766079	−	0.335641i	0.922071	−	0.387020i	$-0.126496\pi$
$853$	−2.23742	−	9.80279i	−0.0766079	−	0.335641i	−0.998679	+	0.0513788i	$0.983638\pi$
$854$	47.2275	+	0.640765i	1.61609	+	0.0219265i
$855$	−1.07699	+	4.71861i	−0.0368323	+	0.161373i
$856$	−5.99798	−	5.56531i	−0.205007	−	0.190218i
$857$	−3.64229	−	0.548987i	−0.124418	−	0.0187530i	0.0865379	−	0.996249i	$-0.472420\pi$
$857$	−3.64229	−	0.548987i	−0.124418	−	0.0187530i	−0.210956	+	0.977496i	$0.567658\pi$
$858$	−0.0720151	−	0.0108545i	−0.00245856	−	0.000370568i
$859$	−20.1589	−	18.7047i	−0.687812	−	0.638197i	0.256769	−	0.966473i	$-0.417342\pi$
$859$	−20.1589	−	18.7047i	−0.687812	−	0.638197i	−0.944582	+	0.328276i	$0.893532\pi$
$860$	1.39345	−	6.10511i	0.0475163	−	0.208183i
$861$	−0.252501	−	0.00342583i	−0.00860520	−	0.000116752i
$862$	−2.32175	−	10.1722i	−0.0790791	−	0.346468i
$863$	19.0051	−	32.9178i	0.646942	−	1.12054i	−0.336908	−	0.941538i	$-0.609381\pi$
$863$	19.0051	−	32.9178i	0.646942	−	1.12054i	0.983849	−	0.178998i	$-0.0572856\pi$
$864$	0.245291	+	0.424857i	0.00834499	+	0.0144539i
$865$	−1.42210	+	1.31951i	−0.0483527	+	0.0448647i
$866$	−22.0357	+	15.0237i	−0.748804	+	0.510526i
$867$	0.135134	−	0.169452i	0.00458939	−	0.00575491i
$868$	−12.1269	−	8.51126i	−0.411615	−	0.288891i
$869$	−10.1994	−	12.7897i	−0.345992	−	0.433861i
$870$	0.0548755	+	0.0169268i	0.00186045	+	0.000573874i
$871$	−3.75499	+	9.56757i	−0.127233	+	0.324185i
$872$	0.280951	+	3.74904i	0.00951421	+	0.126958i
$873$	−4.39144	−	11.1892i	−0.148628	−	0.378697i
$874$	−7.27783	+	3.50482i	−0.246176	+	0.118552i
$875$	−1.57694	+	17.7989i	−0.0533101	+	0.601713i
$876$	−0.0480723	−	0.0231504i	−0.00162421	−	0.000782179i
$877$	0.278259	−	3.71310i	0.00939613	−	0.125383i	−0.990533	−	0.137274i	$-0.956166\pi$
$877$	0.278259	−	3.71310i	0.00939613	−	0.125383i	0.999929	+	0.0118910i	$0.00378510\pi$
$878$	41.2818	−	12.7338i	1.39319	−	0.429743i
$879$	−0.295431	−	0.201421i	−0.00996462	−	0.00679377i
$880$	−10.7872	+	1.62591i	−0.363636	+	0.0548093i
$881$	−16.9864			−0.572288			−0.286144	−	0.958187i	$-0.592374\pi$
$881$	−16.9864			−0.572288			−0.286144	+	0.958187i	$0.592374\pi$
$882$	27.2345	+	26.6809i	0.917032	+	0.898394i
$883$	18.2495			0.614144			0.307072	−	0.951686i	$-0.400651\pi$
$883$	18.2495			0.614144			0.307072	+	0.951686i	$0.400651\pi$
$884$	−0.464477	+	0.0700087i	−0.0156221	+	0.00235465i
$885$	−0.108717	−	0.0741219i	−0.00365448	−	0.00249158i
$886$	−30.6467	+	9.45324i	−1.02959	+	0.317588i
$887$	−0.931735	+	12.4331i	−0.0312846	+	0.417464i	0.959471	+	0.281807i	$0.0909337\pi$
$887$	−0.931735	+	12.4331i	−0.0312846	+	0.417464i	−0.990756	+	0.135657i	$0.956685\pi$
$888$	0.0683507	+	0.0329160i	0.00229370	+	0.00110459i
$889$	6.43543	+	17.0748i	0.215837	+	0.572670i
$890$	2.42048	−	1.16564i	0.0811347	−	0.0390724i
$891$	−10.2635	−	26.1509i	−0.343839	−	0.876087i
$892$	0.462845	+	6.17624i	0.0154972	+	0.206796i
$893$	3.66104	−	9.32819i	0.122512	−	0.312156i
$894$	−0.428394	−	0.132142i	−0.0143276	−	0.00441949i
$895$	−0.436250	−	0.547040i	−0.0145822	−	0.0182855i
$896$	9.58567	−	23.4821i	0.320235	−	0.784481i
$897$	0.0157144	−	0.0197053i	0.000524690	−	0.000657941i
$898$	26.7561	−	18.2420i	0.892862	−	0.608743i
$899$	−10.9568	+	10.1664i	−0.365429	+	0.339068i
$900$	−8.73901	−	15.1364i	−0.291300	−	0.504547i
$901$	0.271820	−	0.470805i	0.00905562	−	0.0156848i
$902$	9.36961	+	41.0510i	0.311974	+	1.36685i
$903$	0.141449	+	0.182393i	0.00470711	+	0.00606966i
$904$	1.64890	−	7.22429i	0.0548415	−	0.240276i
$905$	−7.14656	−	6.63104i	−0.237560	−	0.220423i
$906$	0.455423	+	0.0686439i	0.0151304	+	0.00228054i
$907$	29.7533	+	4.48460i	0.987944	+	0.148909i	0.623085	−	0.782154i	$-0.285879\pi$
$907$	29.7533	+	4.48460i	0.987944	+	0.148909i	0.364859	+	0.931063i	$0.381117\pi$
$908$	16.1548	+	14.9895i	0.536116	+	0.497443i
$909$	0.487661	−	2.13658i	0.0161747	−	0.0708659i
$910$	2.16663	−	2.64252i	0.0718232	−	0.0875986i
$911$	−6.77623	−	29.6886i	−0.224507	−	0.983627i	−0.954039	−	0.299682i	$-0.903120\pi$
$911$	−6.77623	−	29.6886i	−0.224507	−	0.983627i	0.729533	−	0.683946i	$-0.239738\pi$
$912$	0.0715712	−	0.123965i	0.00236996	−	0.00410489i
$913$	−25.9720	−	44.9848i	−0.859547	−	1.48878i
$914$	−13.1212	+	12.1747i	−0.434009	+	0.402702i
$915$	−0.0742529	+	0.0506248i	−0.00245472	+	0.00167360i
$916$	−21.1518	+	26.5236i	−0.698876	+	0.876363i
$917$	−14.6604	+	13.2374i	−0.484131	+	0.437136i
$918$	0.0316171	+	0.0396466i	0.00104352	+	0.00130853i
$919$	33.9759	+	10.4802i	1.12076	+	0.345709i	0.799131	−	0.601156i	$-0.205293\pi$
$919$	33.9759	+	10.4802i	1.12076	+	0.345709i	0.321630	+	0.946865i	$0.395769\pi$
$920$	0.651196	−	1.65922i	0.0214693	−	0.0547029i
$921$	0.0192218	+	0.256497i	0.000633380	+	0.00845186i
$922$	−9.75543	−	24.8564i	−0.321278	−	0.818603i
$923$	−10.1942	+	4.90927i	−0.335546	+	0.161591i
$924$	−0.0704060	+	0.118214i	−0.00231619	+	0.00388894i
$925$	−18.7162	−	9.01326i	−0.615386	−	0.296354i
$926$	4.81500	−	64.2517i	0.158231	−	2.11144i
$927$	−37.9450	+	11.7045i	−1.24628	+	0.384426i
$928$	18.1957	+	12.4056i	0.597303	+	0.407234i
$929$	3.56828	−	0.537832i	0.117072	−	0.0176457i	−0.0902451	−	0.995920i	$-0.528765\pi$
$929$	3.56828	−	0.537832i	0.117072	−	0.0176457i	0.207317	+	0.978274i	$0.433527\pi$
$930$	0.0716768			0.00235037
$931$	3.95142	−	15.3766i	0.129502	−	0.503949i
$932$	1.61417			0.0528738
$933$	−0.207945	+	0.0313427i	−0.00680782	+	0.00102611i
$934$	−61.6417	−	42.0266i	−2.01698	−	1.37515i
$935$	−0.768882	+	0.237169i	−0.0251451	+	0.00775624i
$936$	0.286348	−	3.82105i	0.00935957	−	0.124895i
$937$	−14.1952	−	6.83604i	−0.463736	−	0.223324i	0.187401	−	0.982283i	$-0.439994\pi$
$937$	−14.1952	−	6.83604i	−0.463736	−	0.223324i	−0.651137	+	0.758960i	$0.725708\pi$
$938$	35.7337	+	34.0697i	1.16675	+	1.11242i
$939$	−0.134455	+	0.0647502i	−0.00438778	+	0.00211304i
$940$	−1.48873	−	3.79323i	−0.0485571	−	0.123722i
$941$	−1.71929	−	22.9424i	−0.0560473	−	0.747899i	−0.952457	−	0.304673i	$-0.901453\pi$
$941$	−1.71929	−	22.9424i	−0.0560473	−	0.747899i	0.896410	−	0.443226i	$-0.146166\pi$
$942$	0.121754	−	0.310225i	0.00396697	−	0.0101077i
$943$	−13.9246	−	4.29517i	−0.453447	−	0.139870i
$944$	−44.0901	−	55.2872i	−1.43501	−	1.79945i
$945$	−0.143162	−	0.0235688i	−0.00465707	−	0.000766693i
$946$	23.9960	−	30.0900i	0.780178	−	0.978312i
$947$	20.0181	−	13.6481i	0.650500	−	0.443504i	−0.192587	−	0.981280i	$-0.561688\pi$
$947$	20.0181	−	13.6481i	0.650500	−	0.443504i	0.843088	+	0.537776i	$0.180735\pi$
$948$	0.0639847	−	0.0593691i	0.00207813	−	0.00192822i
$949$	1.60154	+	2.77394i	0.0519880	+	0.0900459i
$950$	−9.25280	+	16.0263i	−0.300200	+	0.519962i
$951$	0.0116066	+	0.0508517i	0.000376369	+	0.00164898i
$952$	0.288626	−	1.18990i	0.00935442	−	0.0385650i
$953$	−4.67149	+	20.4671i	−0.151324	+	0.662996i	0.841177	+	0.540760i	$0.181863\pi$
$953$	−4.67149	+	20.4671i	−0.151324	+	0.662996i	−0.992501	+	0.122235i	$0.960994\pi$
$954$	−5.99089	−	5.55874i	−0.193962	−	0.179971i
$955$	8.08299	+	1.21831i	0.261559	+	0.0394237i
$956$	−23.8170	−	3.58983i	−0.770297	−	0.116104i
$957$	0.101754	+	0.0944143i	0.00328925	+	0.00305198i
$958$	−9.92723	+	43.4940i	−0.320734	+	1.40523i
$959$	−1.23472	−	5.76938i	−0.0398713	−	0.186303i
$960$	−0.00351890	−	0.0154173i	−0.000113572	−	0.000497591i
$961$	6.17214	−	10.6905i	0.199101	−	0.344854i
$962$	4.19639	+	7.26835i	0.135297	+	0.234341i
$963$	−14.0864	+	13.0703i	−0.453929	+	0.421185i
$964$	−2.70000	+	1.84083i	−0.0869612	+	0.0592891i
$965$	−6.33830	+	7.94798i	−0.204037	+	0.255855i
$966$	−0.0591080	−	0.105663i	−0.00190177	−	0.00339965i
$967$	−11.8453	−	14.8535i	−0.380919	−	0.477658i	0.554001	−	0.832516i	$-0.313101\pi$
$967$	−11.8453	−	14.8535i	−0.380919	−	0.477658i	−0.934920	+	0.354858i	$0.884529\pi$
$968$	1.52999	+	0.471941i	0.0491759	+	0.0151688i
$969$	0.00385724	−	0.00982808i	0.000123912	−	0.000315723i
$970$	0.386747	+	5.16078i	0.0124177	+	0.165703i
$971$	11.9983	+	30.5711i	0.385043	+	0.981074i	0.983660	+	0.180038i	$0.0576222\pi$
$971$	11.9983	+	30.5711i	0.385043	+	0.981074i	−0.598616	+	0.801036i	$0.704283\pi$
$972$	0.405191	−	0.195130i	0.0129965	−	0.00625879i
$973$	8.73305	−	5.78212i	0.279969	−	0.185366i
$974$	44.2056	+	21.2883i	1.41644	+	0.682121i
$975$	0.00431496	−	0.0575791i	0.000138189	−	0.00184401i
$976$	−46.1521	+	14.2360i	−1.47729	+	0.455684i
$977$	2.93769	+	2.00288i	0.0939849	+	0.0640778i	0.609401	−	0.792862i	$-0.291410\pi$
$977$	2.93769	+	2.00288i	0.0939849	+	0.0640778i	−0.515416	+	0.856940i	$0.672362\pi$
$978$	0.380821	−	0.0573996i	0.0121773	−	0.00183544i
$979$	6.49375			0.207541
$980$	−3.07509	−	5.67652i	−0.0982303	−	0.181330i
$981$	8.82941			0.281902
$982$	10.9567	−	1.65146i	0.349642	−	0.0527001i
$983$	7.25372	+	4.94550i	0.231358	+	0.157737i	0.673451	−	0.739232i	$-0.264811\pi$
$983$	7.25372	+	4.94550i	0.231358	+	0.157737i	−0.442093	+	0.896969i	$0.645764\pi$
$984$	0.116498	−	0.0359349i	0.00371382	−	0.00114556i
$985$	−0.627069	+	8.36765i	−0.0199801	+	0.266616i
$986$	2.05094	+	0.987682i	0.0653153	+	0.0314542i
$987$	0.142909	+	0.0462141i	0.00454886	+	0.00147101i
$988$	2.64926	−	1.27582i	0.0842843	−	0.0405892i
$989$	4.86604	+	12.3985i	0.154731	+	0.394249i
$990$	0.903935	+	12.0622i	0.0287290	+	0.383361i
$991$	19.4944	−	49.6709i	0.619259	−	1.57785i	−0.184461	−	0.982840i	$-0.559054\pi$
$991$	19.4944	−	49.6709i	0.619259	−	1.57785i	0.803720	−	0.595007i	$-0.202851\pi$
$992$	26.2658	+	8.10193i	0.833940	+	0.257236i
$993$	−0.0111995	−	0.0140437i	−0.000355405	−	0.000445664i
$994$	3.32608	+	54.2504i	0.105497	+	1.72072i
$995$	6.45655	−	8.09626i	0.204686	−	0.256669i
$996$	0.229000	−	0.156129i	0.00725613	−	0.00494714i
$997$	12.1072	−	11.2339i	0.383440	−	0.355780i	−0.464778	−	0.885427i	$-0.653866\pi$
$997$	12.1072	−	11.2339i	0.383440	−	0.355780i	0.848218	+	0.529647i	$0.177676\pi$
$998$	−15.8606	−	27.4714i	−0.502058	−	0.869590i
$999$	0.178173	−	0.308605i	0.00563714	−	0.00976382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.534.8	yes	348
49.39	even	21	inner	637.2.bl.b.235.8	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.235.8	✓	348	49.39	even	21	inner
637.2.bl.b.534.8	yes	348	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79534 + 0.270604i) q^{2} +(-0.0106159 - 0.00723782i) q^{3} +(1.23888 - 0.382145i) q^{4} +(0.0531607 - 0.709380i) q^{5} +(0.0210178 + 0.0101216i) q^{6} +(-2.62131 + 0.358800i) q^{7} +(1.15083 - 0.554210i) q^{8} +(-1.09596 - 2.79247i) q^{9} +O(q^{10})\)	\(q+(-1.79534 + 0.270604i) q^{2} +(-0.0106159 - 0.00723782i) q^{3} +(1.23888 - 0.382145i) q^{4} +(0.0531607 - 0.709380i) q^{5} +(0.0210178 + 0.0101216i) q^{6} +(-2.62131 + 0.358800i) q^{7} +(1.15083 - 0.554210i) q^{8} +(-1.09596 - 2.79247i) q^{9} +(0.0965197 + 1.28797i) q^{10} +(-1.14057 + 2.90613i) q^{11} +(-0.0159178 - 0.00490998i) q^{12} +(0.623490 + 0.781831i) q^{13} +(4.60905 - 1.35351i) q^{14} +(-0.00569871 + 0.00714596i) q^{15} +(-4.05857 + 2.76708i) q^{16} +(-0.265590 + 0.246431i) q^{17} +(2.72328 + 4.71686i) q^{18} +(1.13402 - 1.96417i) q^{19} +(-0.205226 - 0.899153i) q^{20} +(0.0304246 + 0.0151636i) q^{21} +(1.26131 - 5.52614i) q^{22} +(1.43798 + 1.33425i) q^{23} +(-0.0162284 - 0.00244604i) q^{24} +(4.44376 + 0.669789i) q^{25} +(-1.33094 - 1.23494i) q^{26} +(-0.0171539 + 0.0751561i) q^{27} +(-3.11038 + 1.44623i) q^{28} +(0.770039 + 3.37376i) q^{29} +(0.00829741 - 0.0143715i) q^{30} +(2.15961 + 3.74056i) q^{31} +(4.66504 - 4.32853i) q^{32} +(0.0331423 - 0.0225960i) q^{33} +(0.410139 - 0.514298i) q^{34} +(0.115175 + 1.87858i) q^{35} +(-2.42489 - 3.04072i) q^{36} +(-4.41717 - 1.36252i) q^{37} +(-1.50443 + 3.83323i) q^{38} +(-0.000960169 - 0.0128126i) q^{39} +(-0.331967 - 0.845837i) q^{40} +(-6.69285 + 3.22311i) q^{41} +(-0.0587258 - 0.0189908i) q^{42} +(6.11744 + 2.94600i) q^{43} +(-0.302473 + 4.03622i) q^{44} +(-2.03918 + 0.629004i) q^{45} +(-2.94272 - 2.00631i) q^{46} +(4.36897 - 0.658517i) q^{47} +0.0631131 q^{48} +(6.74252 - 1.88105i) q^{49} -8.15932 q^{50} +(0.00460310 - 0.000693806i) q^{51} +(1.07120 + 0.730334i) q^{52} +(-1.43383 + 0.442278i) q^{53} +(0.0104595 - 0.139573i) q^{54} +(2.00092 + 0.963591i) q^{55} +(-2.81783 + 1.86567i) q^{56} +(-0.0262550 + 0.0126437i) q^{57} +(-2.29544 - 5.84868i) q^{58} +(1.07582 + 14.3558i) q^{59} +(-0.00432924 + 0.0110307i) q^{60} +(9.39560 + 2.89816i) q^{61} +(-4.88946 - 6.13119i) q^{62} +(3.87480 + 6.92669i) q^{63} +(-1.07874 + 1.35270i) q^{64} +(0.587761 - 0.400728i) q^{65} +(-0.0533871 + 0.0495360i) q^{66} +(5.13903 + 8.90106i) q^{67} +(-0.234862 + 0.406793i) q^{68} +(-0.00560842 - 0.0245721i) q^{69} +(-0.715130 - 3.34152i) q^{70} +(-2.51776 + 11.0310i) q^{71} +(-2.80888 - 2.60626i) q^{72} +(3.16729 + 0.477393i) q^{73} +(8.29903 + 1.25088i) q^{74} +(-0.0423268 - 0.0392735i) q^{75} +(0.654314 - 2.86674i) q^{76} +(1.94707 - 8.02710i) q^{77} +(0.00519097 + 0.0227431i) q^{78} +(-2.61995 + 4.53789i) q^{79} +(1.74716 + 3.02617i) q^{80} +(-6.59638 + 6.12054i) q^{81} +(11.1438 - 7.59769i) q^{82} +(-10.3738 + 13.0084i) q^{83} +(0.0434871 + 0.00715928i) q^{84} +(0.160694 + 0.201504i) q^{85} +(-11.7801 - 3.63368i) q^{86} +(0.0162440 - 0.0413890i) q^{87} +(0.298003 + 3.97658i) q^{88} +(-0.759924 - 1.93625i) q^{89} +(3.49082 - 1.68109i) q^{90} +(-1.91488 - 1.82571i) q^{91} +(2.29136 + 1.10346i) q^{92} +(0.00414719 - 0.0553404i) q^{93} +(-7.66560 + 2.36453i) q^{94} +(-1.33306 - 0.908865i) q^{95} +(-0.0808528 + 0.0121866i) q^{96} +4.00692 q^{97} +(-11.5961 + 5.20169i) q^{98} +9.36530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more